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Label Class Base field Conductor norm Rank Torsion CM Sato-Tate Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
5.1-a1 5.1-a 4.4.13025.1 \( 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.232009039$ $5.797857315$ 1.814239378 \( \frac{16082288916904829}{100} a^{3} + \frac{20149313773541919}{50} a^{2} - \frac{25854498830773729}{50} a - \frac{133033069069667459}{100} \) \( \bigl[-\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{1}{2} a - \frac{25}{4}\) , \( -\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{1}{2} a - \frac{29}{4}\) , \( a^{2} - a - 5\) , \( -\frac{2735}{4} a^{3} + \frac{3951}{2} a^{2} + \frac{8953}{2} a - \frac{42055}{4}\) , \( -\frac{89057}{4} a^{3} + \frac{128577}{2} a^{2} + \frac{291655}{2} a - \frac{1368261}{4}\bigr] \) ${y}^2+\left(-\frac{1}{4}a^{3}+\frac{3}{2}a^{2}+\frac{1}{2}a-\frac{25}{4}\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}+\frac{3}{2}a^{2}+\frac{1}{2}a-\frac{29}{4}\right){x}^{2}+\left(-\frac{2735}{4}a^{3}+\frac{3951}{2}a^{2}+\frac{8953}{2}a-\frac{42055}{4}\right){x}-\frac{89057}{4}a^{3}+\frac{128577}{2}a^{2}+\frac{291655}{2}a-\frac{1368261}{4}$
5.1-a2 5.1-a 4.4.13025.1 \( 5 \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $0.558002259$ $1484.251472$ 1.814239378 \( \frac{8521}{100} a^{3} + \frac{21131}{50} a^{2} - \frac{321}{50} a + \frac{159009}{100} \) \( \bigl[-\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{1}{2} a - \frac{25}{4}\) , \( -\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{1}{2} a - \frac{29}{4}\) , \( a^{2} - a - 5\) , \( -\frac{15}{2} a^{3} + 23 a^{2} + 44 a - \frac{225}{2}\) , \( \frac{43}{4} a^{3} - \frac{59}{2} a^{2} - \frac{153}{2} a + \frac{671}{4}\bigr] \) ${y}^2+\left(-\frac{1}{4}a^{3}+\frac{3}{2}a^{2}+\frac{1}{2}a-\frac{25}{4}\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}+\frac{3}{2}a^{2}+\frac{1}{2}a-\frac{29}{4}\right){x}^{2}+\left(-\frac{15}{2}a^{3}+23a^{2}+44a-\frac{225}{2}\right){x}+\frac{43}{4}a^{3}-\frac{59}{2}a^{2}-\frac{153}{2}a+\frac{671}{4}$
5.1-a3 5.1-a 4.4.13025.1 \( 5 \) $1$ $\Z/8\Z$ $\mathrm{SU}(2)$ $1.116004519$ $1484.251472$ 1.814239378 \( \frac{5130041}{20} a^{3} - \frac{7395123}{10} a^{2} - \frac{16865103}{10} a + \frac{78990821}{20} \) \( \bigl[1\) , \( \frac{1}{4} a^{3} - \frac{3}{2} a^{2} - \frac{3}{2} a + \frac{25}{4}\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{1}{2} a + \frac{5}{4}\) , \( \frac{61}{2} a^{3} - 103 a^{2} - 113 a + \frac{721}{2}\) , \( -\frac{1013}{4} a^{3} + \frac{1731}{2} a^{2} + \frac{1871}{2} a - \frac{12089}{4}\bigr] \) ${y}^2+{x}{y}+\left(\frac{1}{4}a^{3}-\frac{1}{2}a^{2}-\frac{1}{2}a+\frac{5}{4}\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{3}{2}a^{2}-\frac{3}{2}a+\frac{25}{4}\right){x}^{2}+\left(\frac{61}{2}a^{3}-103a^{2}-113a+\frac{721}{2}\right){x}-\frac{1013}{4}a^{3}+\frac{1731}{2}a^{2}+\frac{1871}{2}a-\frac{12089}{4}$
5.1-a4 5.1-a 4.4.13025.1 \( 5 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.279001129$ $1484.251472$ 1.814239378 \( -\frac{5243081}{20} a^{3} - \frac{2114437}{10} a^{2} + \frac{27643383}{10} a + \frac{84189419}{20} \) \( \bigl[\frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + \frac{9}{4}\) , \( -a - 1\) , \( a^{2} - 5\) , \( -\frac{7}{2} a^{3} + a^{2} + 12 a - \frac{5}{2}\) , \( \frac{39}{4} a^{3} + \frac{27}{2} a^{2} - \frac{65}{2} a - \frac{177}{4}\bigr] \) ${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+\frac{9}{4}\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-\frac{7}{2}a^{3}+a^{2}+12a-\frac{5}{2}\right){x}+\frac{39}{4}a^{3}+\frac{27}{2}a^{2}-\frac{65}{2}a-\frac{177}{4}$
5.1-a5 5.1-a 4.4.13025.1 \( 5 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.116004519$ $92.76571705$ 1.814239378 \( \frac{3544909651}{2500} a^{3} + \frac{1336211879}{250} a^{2} - \frac{5524619889}{1250} a - \frac{44521344553}{2500} \) \( \bigl[\frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + \frac{9}{4}\) , \( -\frac{1}{4} a^{3} + \frac{1}{2} a^{2} + \frac{1}{2} a - \frac{1}{4}\) , \( a^{2} - 5\) , \( -4 a^{2} - 25 a - 29\) , \( -\frac{1}{4} a^{3} - \frac{41}{2} a^{2} - \frac{179}{2} a - \frac{389}{4}\bigr] \) ${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+\frac{9}{4}\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}+\frac{1}{2}a^{2}+\frac{1}{2}a-\frac{1}{4}\right){x}^{2}+\left(-4a^{2}-25a-29\right){x}-\frac{1}{4}a^{3}-\frac{41}{2}a^{2}-\frac{179}{2}a-\frac{389}{4}$
5.1-a6 5.1-a 4.4.13025.1 \( 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.232009039$ $5.797857315$ 1.814239378 \( -\frac{393118916044291297}{312500} a^{3} + \frac{3366097771500863977}{781250} a^{2} + \frac{3630721974525889001}{781250} a - \frac{23505911313760565541}{1562500} \) \( \bigl[\frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + \frac{9}{4}\) , \( -\frac{1}{4} a^{3} + \frac{1}{2} a^{2} + \frac{1}{2} a - \frac{1}{4}\) , \( a^{2} - 5\) , \( -\frac{15}{4} a^{3} - \frac{23}{2} a^{2} + \frac{45}{2} a + \frac{249}{4}\) , \( 32 a^{3} - 11 a^{2} - 411 a - 521\bigr] \) ${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+\frac{9}{4}\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}+\frac{1}{2}a^{2}+\frac{1}{2}a-\frac{1}{4}\right){x}^{2}+\left(-\frac{15}{4}a^{3}-\frac{23}{2}a^{2}+\frac{45}{2}a+\frac{249}{4}\right){x}+32a^{3}-11a^{2}-411a-521$
5.2-a1 5.2-a 4.4.13025.1 \( 5 \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $0.558002259$ $1484.251472$ 1.814239378 \( \frac{3281}{5} a^{3} - \frac{47636}{25} a^{2} - \frac{111051}{25} a + \frac{331311}{25} \) \( \bigl[-\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{1}{2} a - \frac{29}{4}\) , \( -\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{1}{2} a - \frac{33}{4}\) , \( a^{2} - a - 5\) , \( -\frac{3}{2} a^{3} - a^{2} + 3 a + \frac{1}{2}\) , \( \frac{1}{2} a^{3} + 5 a^{2} - 2 a - \frac{37}{2}\bigr] \) ${y}^2+\left(-\frac{1}{4}a^{3}+\frac{3}{2}a^{2}+\frac{1}{2}a-\frac{29}{4}\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}+\frac{3}{2}a^{2}+\frac{1}{2}a-\frac{33}{4}\right){x}^{2}+\left(-\frac{3}{2}a^{3}-a^{2}+3a+\frac{1}{2}\right){x}+\frac{1}{2}a^{3}+5a^{2}-2a-\frac{37}{2}$
5.2-a2 5.2-a 4.4.13025.1 \( 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.232009039$ $5.797857315$ 1.814239378 \( \frac{8162587691254533}{10} a^{3} - \frac{58928739801496039}{25} a^{2} - \frac{133634999328788374}{25} a + \frac{626977241040462753}{50} \) \( \bigl[-\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{3}{2} a - \frac{29}{4}\) , \( -a^{2} + 2 a + 7\) , \( a\) , \( -\frac{21}{2} a^{3} - 53 a^{2} - 11 a + \frac{191}{2}\) , \( -\frac{473}{2} a^{3} - 741 a^{2} + 251 a + \frac{3045}{2}\bigr] \) ${y}^2+\left(-\frac{1}{4}a^{3}+\frac{3}{2}a^{2}+\frac{3}{2}a-\frac{29}{4}\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+2a+7\right){x}^{2}+\left(-\frac{21}{2}a^{3}-53a^{2}-11a+\frac{191}{2}\right){x}-\frac{473}{2}a^{3}-741a^{2}+251a+\frac{3045}{2}$
5.2-a3 5.2-a 4.4.13025.1 \( 5 \) $1$ $\Z/8\Z$ $\mathrm{SU}(2)$ $1.116004519$ $1484.251472$ 1.814239378 \( \frac{248732}{5} a^{3} + \frac{635077}{5} a^{2} - \frac{754902}{5} a - 402850 \) \( \bigl[1\) , \( -\frac{1}{2} a^{3} + 2 a^{2} + 3 a - \frac{17}{2}\) , \( a\) , \( \frac{63}{4} a^{3} + \frac{25}{2} a^{2} - \frac{331}{2} a - \frac{981}{4}\) , \( -\frac{227}{2} a^{3} - 90 a^{2} + 1195 a + \frac{3617}{2}\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+2a^{2}+3a-\frac{17}{2}\right){x}^{2}+\left(\frac{63}{4}a^{3}+\frac{25}{2}a^{2}-\frac{331}{2}a-\frac{981}{4}\right){x}-\frac{227}{2}a^{3}-90a^{2}+1195a+\frac{3617}{2}$
5.2-a4 5.2-a 4.4.13025.1 \( 5 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.116004519$ $92.76571705$ 1.814239378 \( \frac{5359729438}{625} a^{3} - \frac{15832443399}{625} a^{2} - \frac{6942686232}{125} a + \frac{85374011842}{625} \) \( \bigl[\frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + \frac{5}{4}\) , \( -\frac{1}{2} a^{3} + 2 a^{2} + a - \frac{19}{2}\) , \( a + 1\) , \( -\frac{417}{4} a^{3} + \frac{601}{2} a^{2} + \frac{1365}{2} a - \frac{6373}{4}\) , \( -\frac{5197}{4} a^{3} + \frac{7501}{2} a^{2} + \frac{17029}{2} a - \frac{79877}{4}\bigr] \) ${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+\frac{5}{4}\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+2a^{2}+a-\frac{19}{2}\right){x}^{2}+\left(-\frac{417}{4}a^{3}+\frac{601}{2}a^{2}+\frac{1365}{2}a-\frac{6373}{4}\right){x}-\frac{5197}{4}a^{3}+\frac{7501}{2}a^{2}+\frac{17029}{2}a-\frac{79877}{4}$
5.2-a5 5.2-a 4.4.13025.1 \( 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.232009039$ $5.797857315$ 1.814239378 \( -\frac{498935338185792737}{781250} a^{3} - \frac{201316257453911009}{390625} a^{2} + \frac{2629836897626618438}{390625} a + \frac{8007337014517619191}{781250} \) \( \bigl[\frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + \frac{5}{4}\) , \( -\frac{1}{2} a^{3} + 2 a^{2} + a - \frac{19}{2}\) , \( a + 1\) , \( -103 a^{3} + 298 a^{2} + 670 a - 1572\) , \( -\frac{5477}{4} a^{3} + \frac{7905}{2} a^{2} + \frac{17945}{2} a - \frac{84169}{4}\bigr] \) ${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+\frac{5}{4}\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+2a^{2}+a-\frac{19}{2}\right){x}^{2}+\left(-103a^{3}+298a^{2}+670a-1572\right){x}-\frac{5477}{4}a^{3}+\frac{7905}{2}a^{2}+\frac{17945}{2}a-\frac{84169}{4}$
5.2-a6 5.2-a 4.4.13025.1 \( 5 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.279001129$ $1484.251472$ 1.814239378 \( -\frac{2580572}{5} a^{3} + \frac{8839903}{5} a^{2} + \frac{9526362}{5} a - 6169442 \) \( \bigl[\frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + \frac{5}{4}\) , \( a^{2} - 2 a - 7\) , \( a\) , \( -\frac{255}{4} a^{3} + \frac{363}{2} a^{2} + \frac{839}{2} a - \frac{3819}{4}\) , \( \frac{1047}{2} a^{3} - 1509 a^{2} - 3432 a + \frac{16037}{2}\bigr] \) ${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+\frac{5}{4}\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-2a-7\right){x}^{2}+\left(-\frac{255}{4}a^{3}+\frac{363}{2}a^{2}+\frac{839}{2}a-\frac{3819}{4}\right){x}+\frac{1047}{2}a^{3}-1509a^{2}-3432a+\frac{16037}{2}$
16.1-a1 16.1-a 4.4.13025.1 \( 2^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.293903604$ $269.2332131$ 2.773349944 \( \frac{3806015913}{4} a^{3} - 2747461755 a^{2} - \frac{12461510553}{2} a + \frac{58463376529}{4} \) \( \bigl[-\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{3}{2} a - \frac{29}{4}\) , \( -\frac{1}{2} a^{3} + 2 a^{2} + a - \frac{17}{2}\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{1}{2} a + \frac{5}{4}\) , \( -\frac{45}{4} a^{3} - \frac{1}{2} a^{2} + \frac{207}{2} a + \frac{483}{4}\) , \( -\frac{2661}{4} a^{3} - \frac{1063}{2} a^{2} + \frac{14001}{2} a + \frac{42535}{4}\bigr] \) ${y}^2+\left(-\frac{1}{4}a^{3}+\frac{3}{2}a^{2}+\frac{3}{2}a-\frac{29}{4}\right){x}{y}+\left(\frac{1}{4}a^{3}-\frac{1}{2}a^{2}-\frac{1}{2}a+\frac{5}{4}\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+2a^{2}+a-\frac{17}{2}\right){x}^{2}+\left(-\frac{45}{4}a^{3}-\frac{1}{2}a^{2}+\frac{207}{2}a+\frac{483}{4}\right){x}-\frac{2661}{4}a^{3}-\frac{1063}{2}a^{2}+\frac{14001}{2}a+\frac{42535}{4}$
16.1-a2 16.1-a 4.4.13025.1 \( 2^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.058780720$ $269.2332131$ 2.773349944 \( \frac{787971}{64} a^{3} + \frac{874133}{32} a^{2} - \frac{734245}{16} a - \frac{6087581}{64} \) \( \bigl[a\) , \( -\frac{1}{2} a^{3} + 2 a^{2} + 3 a - \frac{15}{2}\) , \( a^{2} - a - 6\) , \( -18 a^{3} - 36 a^{2} + 60 a + 121\) , \( 142 a^{3} + 366 a^{2} - 457 a - 1212\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+2a^{2}+3a-\frac{15}{2}\right){x}^{2}+\left(-18a^{3}-36a^{2}+60a+121\right){x}+142a^{3}+366a^{2}-457a-1212$
16.1-b1 16.1-b 4.4.13025.1 \( 2^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.044095954$ $165.6929729$ 2.816868993 \( \frac{65814678933}{2048} a^{3} - \frac{225387636239}{2048} a^{2} - \frac{243146393173}{2048} a + \frac{786975616815}{2048} \) \( \bigl[-\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{1}{2} a - \frac{25}{4}\) , \( -a - 1\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{1}{2} a + \frac{9}{4}\) , \( \frac{39}{2} a^{3} - 76 a^{2} - 72 a + \frac{531}{2}\) , \( -\frac{415}{4} a^{3} + \frac{667}{2} a^{2} + \frac{763}{2} a - \frac{4667}{4}\bigr] \) ${y}^2+\left(-\frac{1}{4}a^{3}+\frac{3}{2}a^{2}+\frac{1}{2}a-\frac{25}{4}\right){x}{y}+\left(\frac{1}{4}a^{3}-\frac{1}{2}a^{2}-\frac{1}{2}a+\frac{9}{4}\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(\frac{39}{2}a^{3}-76a^{2}-72a+\frac{531}{2}\right){x}-\frac{415}{4}a^{3}+\frac{667}{2}a^{2}+\frac{763}{2}a-\frac{4667}{4}$
16.1-c1 16.1-c 4.4.13025.1 \( 2^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.021195184$ $3660.981213$ 2.719604970 \( 939910 a^{3} - \frac{6754329}{2} a^{2} - 3485046 a + 11778016 \) \( \bigl[a^{2} - 6\) , \( -\frac{1}{2} a^{3} + 2 a^{2} + a - \frac{17}{2}\) , \( 1\) , \( \frac{1}{2} a^{3} + 7 a^{2} - 13 a - \frac{89}{2}\) , \( -9 a^{3} - a^{2} + 88 a + 109\bigr] \) ${y}^2+\left(a^{2}-6\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+2a^{2}+a-\frac{17}{2}\right){x}^{2}+\left(\frac{1}{2}a^{3}+7a^{2}-13a-\frac{89}{2}\right){x}-9a^{3}-a^{2}+88a+109$
16.1-d1 16.1-d 4.4.13025.1 \( 2^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $21.12375869$ 0.185089734 \( \frac{181766666214515}{64} a^{3} + \frac{113866544096805}{16} a^{2} - \frac{146107414893665}{16} a - \frac{1503577557583359}{64} \) \( \bigl[1\) , \( -\frac{1}{4} a^{3} + \frac{1}{2} a^{2} + \frac{1}{2} a - \frac{5}{4}\) , \( a^{2} - 6\) , \( \frac{143}{2} a^{3} - 246 a^{2} - 261 a + \frac{1709}{2}\) , \( \frac{3943}{4} a^{3} - \frac{6755}{2} a^{2} - \frac{7279}{2} a + \frac{47147}{4}\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}+\frac{1}{2}a^{2}+\frac{1}{2}a-\frac{5}{4}\right){x}^{2}+\left(\frac{143}{2}a^{3}-246a^{2}-261a+\frac{1709}{2}\right){x}+\frac{3943}{4}a^{3}-\frac{6755}{2}a^{2}-\frac{7279}{2}a+\frac{47147}{4}$
16.1-d2 16.1-d 4.4.13025.1 \( 2^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $21.12375869$ 0.185089734 \( \frac{461279441127405}{32} a^{3} - \frac{1332058636662935}{32} a^{2} - \frac{3020761815620645}{32} a + \frac{7086273491879023}{32} \) \( \bigl[1\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{1}{2} a + \frac{1}{4}\) , \( a^{2} - 6\) , \( 36 a^{3} + 32 a^{2} - 386 a - 603\) , \( \frac{1763}{4} a^{3} + \frac{709}{2} a^{2} - \frac{9297}{2} a - \frac{28305}{4}\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{1}{2}a^{2}-\frac{1}{2}a+\frac{1}{4}\right){x}^{2}+\left(36a^{3}+32a^{2}-386a-603\right){x}+\frac{1763}{4}a^{3}+\frac{709}{2}a^{2}-\frac{9297}{2}a-\frac{28305}{4}$
16.1-e1 16.1-e 4.4.13025.1 \( 2^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.021195184$ $3660.981213$ 2.719604970 \( \frac{2844041}{8} a^{3} + \frac{3145337}{4} a^{2} - \frac{17149779}{4} a - \frac{79619339}{8} \) \( \bigl[-\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{1}{2} a - \frac{29}{4}\) , \( a^{2} - 5\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{1}{2} a + \frac{9}{4}\) , \( -\frac{1}{2} a^{3} + 3 a^{2} + 3 a - \frac{21}{2}\) , \( \frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - \frac{3}{4}\bigr] \) ${y}^2+\left(-\frac{1}{4}a^{3}+\frac{3}{2}a^{2}+\frac{1}{2}a-\frac{29}{4}\right){x}{y}+\left(\frac{1}{4}a^{3}-\frac{1}{2}a^{2}-\frac{1}{2}a+\frac{9}{4}\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(-\frac{1}{2}a^{3}+3a^{2}+3a-\frac{21}{2}\right){x}+\frac{1}{4}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-\frac{3}{4}$
16.1-f1 16.1-f 4.4.13025.1 \( 2^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.044095954$ $165.6929729$ 2.816868993 \( \frac{66862780519}{4096} a^{3} + \frac{13447748927}{1024} a^{2} - \frac{176165010991}{1024} a - \frac{1071630086699}{4096} \) \( \bigl[-\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{1}{2} a - \frac{29}{4}\) , \( -a^{2} + 2 a + 5\) , \( a\) , \( \frac{7}{2} a^{3} + 30 a^{2} - 68 a - \frac{571}{2}\) , \( -69 a^{3} + 11 a^{2} + 655 a + 538\bigr] \) ${y}^2+\left(-\frac{1}{4}a^{3}+\frac{3}{2}a^{2}+\frac{1}{2}a-\frac{29}{4}\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+2a+5\right){x}^{2}+\left(\frac{7}{2}a^{3}+30a^{2}-68a-\frac{571}{2}\right){x}-69a^{3}+11a^{2}+655a+538$
16.1-g1 16.1-g 4.4.13025.1 \( 2^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.293903604$ $269.2332131$ 2.773349944 \( \frac{1501846221}{8} a^{3} + \frac{1875968973}{4} a^{2} - \frac{2418613035}{4} a - \frac{12376851655}{8} \) \( \bigl[a^{2} - 6\) , \( -\frac{1}{2} a^{3} + 2 a^{2} + a - \frac{15}{2}\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{1}{2} a + \frac{9}{4}\) , \( -20 a^{3} + 69 a^{2} + 76 a - 243\) , \( -\frac{5515}{4} a^{3} + \frac{9447}{2} a^{2} + \frac{10195}{2} a - \frac{65999}{4}\bigr] \) ${y}^2+\left(a^{2}-6\right){x}{y}+\left(\frac{1}{4}a^{3}-\frac{1}{2}a^{2}-\frac{1}{2}a+\frac{9}{4}\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+2a^{2}+a-\frac{15}{2}\right){x}^{2}+\left(-20a^{3}+69a^{2}+76a-243\right){x}-\frac{5515}{4}a^{3}+\frac{9447}{2}a^{2}+\frac{10195}{2}a-\frac{65999}{4}$
16.1-g2 16.1-g 4.4.13025.1 \( 2^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.058780720$ $269.2332131$ 2.773349944 \( \frac{7457677}{128} a^{3} - \frac{10781885}{64} a^{2} - \frac{24163877}{64} a + \frac{113893029}{128} \) \( \bigl[\frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{1}{2} a + \frac{9}{4}\) , \( -\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{3}{2} a - \frac{29}{4}\) , \( -\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{3}{2} a - \frac{25}{4}\) , \( -85 a^{3} + 248 a^{2} + 558 a - 1309\) , \( \frac{2143}{2} a^{3} - 3089 a^{2} - 7013 a + \frac{32879}{2}\bigr] \) ${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{2}a^{2}-\frac{1}{2}a+\frac{9}{4}\right){x}{y}+\left(-\frac{1}{4}a^{3}+\frac{3}{2}a^{2}+\frac{3}{2}a-\frac{25}{4}\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}+\frac{3}{2}a^{2}+\frac{3}{2}a-\frac{29}{4}\right){x}^{2}+\left(-85a^{3}+248a^{2}+558a-1309\right){x}+\frac{2143}{2}a^{3}-3089a^{2}-7013a+\frac{32879}{2}$
19.1-a1 19.1-a 4.4.13025.1 \( 19 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $576.6063225$ 1.263079082 \( -\frac{891615}{76} a^{3} + \frac{2041049}{38} a^{2} + \frac{15107559}{38} a + \frac{36528405}{76} \) \( \bigl[a\) , \( -\frac{1}{2} a^{3} + 2 a^{2} + a - \frac{15}{2}\) , \( a^{2} - a - 5\) , \( -\frac{5}{2} a^{3} - a^{2} + 9 a + \frac{11}{2}\) , \( \frac{73}{4} a^{3} - \frac{79}{2} a^{2} - \frac{133}{2} a + \frac{553}{4}\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+2a^{2}+a-\frac{15}{2}\right){x}^{2}+\left(-\frac{5}{2}a^{3}-a^{2}+9a+\frac{11}{2}\right){x}+\frac{73}{4}a^{3}-\frac{79}{2}a^{2}-\frac{133}{2}a+\frac{553}{4}$
19.1-a2 19.1-a 4.4.13025.1 \( 19 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $72.07579031$ 1.263079082 \( -\frac{19375894269482259}{521284} a^{3} + \frac{33181388674512829}{260642} a^{2} + \frac{35789925592353663}{260642} a - \frac{231710074739308823}{521284} \) \( \bigl[\frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + \frac{9}{4}\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a + \frac{5}{4}\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + \frac{9}{4}\) , \( -\frac{7}{4} a^{3} + \frac{7}{2} a^{2} + \frac{33}{2} a - \frac{103}{4}\) , \( -7 a^{3} + 19 a^{2} + 54 a - 122\bigr] \) ${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+\frac{9}{4}\right){x}{y}+\left(\frac{1}{4}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+\frac{9}{4}\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{1}{2}a^{2}-\frac{5}{2}a+\frac{5}{4}\right){x}^{2}+\left(-\frac{7}{4}a^{3}+\frac{7}{2}a^{2}+\frac{33}{2}a-\frac{103}{4}\right){x}-7a^{3}+19a^{2}+54a-122$
19.1-a3 19.1-a 4.4.13025.1 \( 19 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1153.212645$ 1.263079082 \( -\frac{75238485}{1444} a^{3} + \frac{128979535}{722} a^{2} + \frac{138372045}{722} a - \frac{895442173}{1444} \) \( \bigl[\frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + \frac{9}{4}\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a + \frac{5}{4}\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + \frac{9}{4}\) , \( -\frac{1}{2} a^{3} + a^{2} + 4 a - \frac{9}{2}\) , \( -1\bigr] \) ${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+\frac{9}{4}\right){x}{y}+\left(\frac{1}{4}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+\frac{9}{4}\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{1}{2}a^{2}-\frac{5}{2}a+\frac{5}{4}\right){x}^{2}+\left(-\frac{1}{2}a^{3}+a^{2}+4a-\frac{9}{2}\right){x}-1$
19.1-a4 19.1-a 4.4.13025.1 \( 19 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $2306.425290$ 1.263079082 \( \frac{139118971}{76} a^{3} - \frac{201258785}{38} a^{2} - \frac{455105151}{38} a + \frac{2143904527}{76} \) \( \bigl[\frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + \frac{9}{4}\) , \( -a^{2} + 5\) , \( a + 1\) , \( 14 a^{3} - 47 a^{2} - 51 a + 165\) , \( 15 a^{3} - 53 a^{2} - 56 a + 184\bigr] \) ${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+\frac{9}{4}\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(14a^{3}-47a^{2}-51a+165\right){x}+15a^{3}-53a^{2}-56a+184$
19.2-a1 19.2-a 4.4.13025.1 \( 19 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $2306.425290$ 1.263079082 \( \frac{27035131}{76} a^{3} + \frac{35104683}{38} a^{2} - \frac{43357155}{38} a - \frac{231925941}{76} \) \( \bigl[\frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + \frac{9}{4}\) , \( a^{2} - 6\) , \( a\) , \( \frac{15}{2} a^{3} + 5 a^{2} - 76 a - \frac{215}{2}\) , \( \frac{7}{2} a^{3} + 3 a^{2} - 36 a - \frac{113}{2}\bigr] \) ${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+\frac{9}{4}\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(\frac{15}{2}a^{3}+5a^{2}-76a-\frac{215}{2}\right){x}+\frac{7}{2}a^{3}+3a^{2}-36a-\frac{113}{2}$
19.2-a2 19.2-a 4.4.13025.1 \( 19 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $72.07579031$ 1.263079082 \( -\frac{9836531269982961}{521284} a^{3} - \frac{3968963135047609}{260642} a^{2} + \frac{51847351026041997}{260642} a + \frac{157865069166857399}{521284} \) \( \bigl[\frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + \frac{9}{4}\) , \( a - 1\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + \frac{9}{4}\) , \( -\frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{9}{2} a - \frac{49}{4}\) , \( -\frac{1}{4} a^{3} - \frac{9}{2} a^{2} - \frac{21}{2} a - \frac{25}{4}\bigr] \) ${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+\frac{9}{4}\right){x}{y}+\left(\frac{1}{4}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+\frac{9}{4}\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-\frac{1}{4}a^{3}+\frac{1}{2}a^{2}-\frac{9}{2}a-\frac{49}{4}\right){x}-\frac{1}{4}a^{3}-\frac{9}{2}a^{2}-\frac{21}{2}a-\frac{25}{4}$
19.2-a3 19.2-a 4.4.13025.1 \( 19 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1153.212645$ 1.263079082 \( -\frac{38298615}{1444} a^{3} - \frac{15442435}{722} a^{2} + \frac{202239255}{722} a + \frac{619319757}{1444} \) \( \bigl[\frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + \frac{9}{4}\) , \( a - 1\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + \frac{9}{4}\) , \( -\frac{1}{4} a^{3} + \frac{1}{2} a^{2} + \frac{1}{2} a - \frac{9}{4}\) , \( -1\bigr] \) ${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+\frac{9}{4}\right){x}{y}+\left(\frac{1}{4}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+\frac{9}{4}\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-\frac{1}{4}a^{3}+\frac{1}{2}a^{2}+\frac{1}{2}a-\frac{9}{4}\right){x}-1$
19.2-a4 19.2-a 4.4.13025.1 \( 19 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $576.6063225$ 1.263079082 \( \frac{7048893}{76} a^{3} - \frac{8198327}{38} a^{2} - \frac{33579393}{38} a + \frac{133280525}{76} \) \( \bigl[\frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{1}{2} a + \frac{9}{4}\) , \( a^{2} - a - 5\) , \( 0\) , \( -\frac{13}{2} a^{3} + 26 a^{2} + 39 a - \frac{281}{2}\) , \( 28 a^{3} - 61 a^{2} - 199 a + 282\bigr] \) ${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{2}a^{2}-\frac{1}{2}a+\frac{9}{4}\right){x}{y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-\frac{13}{2}a^{3}+26a^{2}+39a-\frac{281}{2}\right){x}+28a^{3}-61a^{2}-199a+282$
20.2-a1 20.2-a 4.4.13025.1 \( 2^{2} \cdot 5 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $236.3617268$ 2.071039052 \( -\frac{41249897}{160} a^{3} - \frac{32874297}{160} a^{2} + \frac{86878237}{32} a + \frac{658504129}{160} \) \( \bigl[a^{2} - a - 6\) , \( -\frac{1}{2} a^{3} + 2 a^{2} + 2 a - \frac{15}{2}\) , \( a\) , \( -\frac{15}{2} a^{3} + 13 a^{2} + 30 a - \frac{81}{2}\) , \( -\frac{29}{2} a^{3} + 177 a^{2} + 65 a - \frac{1213}{2}\bigr] \) ${y}^2+\left(a^{2}-a-6\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+2a^{2}+2a-\frac{15}{2}\right){x}^{2}+\left(-\frac{15}{2}a^{3}+13a^{2}+30a-\frac{81}{2}\right){x}-\frac{29}{2}a^{3}+177a^{2}+65a-\frac{1213}{2}$
20.2-a2 20.2-a 4.4.13025.1 \( 2^{2} \cdot 5 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $236.3617268$ 2.071039052 \( -\frac{1585257}{250} a^{3} - \frac{5800377}{250} a^{2} + \frac{958521}{10} a + \frac{55242049}{250} \) \( \bigl[a^{2} - 5\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a + \frac{5}{4}\) , \( a^{2} - 6\) , \( \frac{3}{2} a^{3} + a^{2} - 15 a - \frac{41}{2}\) , \( -\frac{9}{2} a^{3} - 4 a^{2} + 45 a + \frac{137}{2}\bigr] \) ${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{1}{2}a^{2}-\frac{5}{2}a+\frac{5}{4}\right){x}^{2}+\left(\frac{3}{2}a^{3}+a^{2}-15a-\frac{41}{2}\right){x}-\frac{9}{2}a^{3}-4a^{2}+45a+\frac{137}{2}$
20.2-b1 20.2-b 4.4.13025.1 \( 2^{2} \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.324409008$ $217.7229630$ 3.094413023 \( -\frac{126809642037}{500} a^{3} - \frac{51181824711}{250} a^{2} + \frac{66841641489}{25} a + \frac{2035411780669}{500} \) \( \bigl[-\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{3}{2} a - \frac{29}{4}\) , \( -\frac{1}{2} a^{3} + 2 a^{2} + 3 a - \frac{19}{2}\) , \( 0\) , \( -\frac{27}{4} a^{3} + \frac{55}{2} a^{2} + \frac{87}{2} a - \frac{603}{4}\) , \( \frac{81}{2} a^{3} - 105 a^{2} - 267 a + \frac{1095}{2}\bigr] \) ${y}^2+\left(-\frac{1}{4}a^{3}+\frac{3}{2}a^{2}+\frac{3}{2}a-\frac{29}{4}\right){x}{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+2a^{2}+3a-\frac{19}{2}\right){x}^{2}+\left(-\frac{27}{4}a^{3}+\frac{55}{2}a^{2}+\frac{87}{2}a-\frac{603}{4}\right){x}+\frac{81}{2}a^{3}-105a^{2}-267a+\frac{1095}{2}$
20.2-b2 20.2-b 4.4.13025.1 \( 2^{2} \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.081102252$ $435.4459260$ 3.094413023 \( -\frac{2005074227}{2000} a^{3} + \frac{3526517969}{1000} a^{2} + \frac{1484491401}{400} a - \frac{3075936147}{250} \) \( \bigl[a^{2} - 6\) , \( -a^{2} + a + 5\) , \( a^{2} - 5\) , \( -\frac{1}{2} a^{3} + a - \frac{3}{2}\) , \( -\frac{1}{4} a^{3} - \frac{3}{2} a^{2} - \frac{3}{2} a + \frac{3}{4}\bigr] \) ${y}^2+\left(a^{2}-6\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(-\frac{1}{2}a^{3}+a-\frac{3}{2}\right){x}-\frac{1}{4}a^{3}-\frac{3}{2}a^{2}-\frac{3}{2}a+\frac{3}{4}$
20.2-b3 20.2-b 4.4.13025.1 \( 2^{2} \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.162204504$ $435.4459260$ 3.094413023 \( -\frac{40663869}{12500} a^{3} - \frac{21974853}{12500} a^{2} + \frac{102869877}{3125} a + \frac{150868966}{3125} \) \( \bigl[a^{2} - 6\) , \( \frac{1}{2} a^{3} - 2 a^{2} - 3 a + \frac{17}{2}\) , \( 1\) , \( \frac{9}{2} a^{3} - 18 a^{2} - 19 a + \frac{137}{2}\) , \( -\frac{61}{4} a^{3} + \frac{91}{2} a^{2} + \frac{109}{2} a - \frac{629}{4}\bigr] \) ${y}^2+\left(a^{2}-6\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{2}a^{3}-2a^{2}-3a+\frac{17}{2}\right){x}^{2}+\left(\frac{9}{2}a^{3}-18a^{2}-19a+\frac{137}{2}\right){x}-\frac{61}{4}a^{3}+\frac{91}{2}a^{2}+\frac{109}{2}a-\frac{629}{4}$
20.2-b4 20.2-b 4.4.13025.1 \( 2^{2} \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.324409008$ $54.43074075$ 3.094413023 \( \frac{1681292977381}{39062500} a^{3} - \frac{444316861553}{3906250} a^{2} - \frac{2690205173457}{9765625} a + \frac{24032472659987}{39062500} \) \( \bigl[\frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{1}{2} a + \frac{9}{4}\) , \( a^{2} - a - 7\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + \frac{5}{4}\) , \( -\frac{271}{4} a^{3} + \frac{457}{2} a^{2} + \frac{505}{2} a - \frac{3171}{4}\) , \( -\frac{2385}{2} a^{3} + 4086 a^{2} + 4404 a - \frac{28539}{2}\bigr] \) ${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{2}a^{2}-\frac{1}{2}a+\frac{9}{4}\right){x}{y}+\left(\frac{1}{4}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+\frac{5}{4}\right){y}={x}^{3}+\left(a^{2}-a-7\right){x}^{2}+\left(-\frac{271}{4}a^{3}+\frac{457}{2}a^{2}+\frac{505}{2}a-\frac{3171}{4}\right){x}-\frac{2385}{2}a^{3}+4086a^{2}+4404a-\frac{28539}{2}$
20.2-c1 20.2-c 4.4.13025.1 \( 2^{2} \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.382186275$ $417.1236793$ 2.793708320 \( \frac{123186}{25} a^{3} - \frac{722261}{50} a^{2} - \frac{800877}{25} a + \frac{3876593}{50} \) \( \bigl[-\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{1}{2} a - \frac{29}{4}\) , \( -\frac{1}{4} a^{3} + \frac{3}{2} a^{2} - \frac{1}{2} a - \frac{29}{4}\) , \( a^{2} - 5\) , \( -\frac{11}{4} a^{3} + \frac{17}{2} a^{2} + \frac{21}{2} a - \frac{123}{4}\) , \( -3 a^{3} + 9 a^{2} + 11 a - 33\bigr] \) ${y}^2+\left(-\frac{1}{4}a^{3}+\frac{3}{2}a^{2}+\frac{1}{2}a-\frac{29}{4}\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}+\frac{3}{2}a^{2}-\frac{1}{2}a-\frac{29}{4}\right){x}^{2}+\left(-\frac{11}{4}a^{3}+\frac{17}{2}a^{2}+\frac{21}{2}a-\frac{123}{4}\right){x}-3a^{3}+9a^{2}+11a-33$
20.2-c2 20.2-c 4.4.13025.1 \( 2^{2} \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.382186275$ $834.2473587$ 2.793708320 \( -\frac{504299519}{10} a^{3} + \frac{9906421751}{10} a^{2} + 252051456 a - \frac{16958255326}{5} \) \( \bigl[-\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{1}{2} a - \frac{29}{4}\) , \( -a^{2} + a + 7\) , \( -\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{3}{2} a - \frac{25}{4}\) , \( \frac{3}{4} a^{3} + \frac{67}{2} a^{2} - \frac{89}{2} a - \frac{1189}{4}\) , \( -13 a^{3} - 120 a^{2} + 254 a + 1135\bigr] \) ${y}^2+\left(-\frac{1}{4}a^{3}+\frac{3}{2}a^{2}+\frac{1}{2}a-\frac{29}{4}\right){x}{y}+\left(-\frac{1}{4}a^{3}+\frac{3}{2}a^{2}+\frac{3}{2}a-\frac{25}{4}\right){y}={x}^{3}+\left(-a^{2}+a+7\right){x}^{2}+\left(\frac{3}{4}a^{3}+\frac{67}{2}a^{2}-\frac{89}{2}a-\frac{1189}{4}\right){x}-13a^{3}-120a^{2}+254a+1135$
20.2-c3 20.2-c 4.4.13025.1 \( 2^{2} \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.191093137$ $1668.494717$ 2.793708320 \( -\frac{40863}{20} a^{3} + \frac{163379}{10} a^{2} + \frac{163893}{20} a - \frac{270887}{5} \) \( \bigl[-\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{1}{2} a - \frac{29}{4}\) , \( -a^{2} + a + 7\) , \( -\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{3}{2} a - \frac{25}{4}\) , \( -\frac{1}{2} a^{3} + a^{2} + 3 a - \frac{17}{2}\) , \( \frac{3}{4} a^{3} + \frac{1}{2} a^{2} - \frac{19}{2} a - \frac{65}{4}\bigr] \) ${y}^2+\left(-\frac{1}{4}a^{3}+\frac{3}{2}a^{2}+\frac{1}{2}a-\frac{29}{4}\right){x}{y}+\left(-\frac{1}{4}a^{3}+\frac{3}{2}a^{2}+\frac{3}{2}a-\frac{25}{4}\right){y}={x}^{3}+\left(-a^{2}+a+7\right){x}^{2}+\left(-\frac{1}{2}a^{3}+a^{2}+3a-\frac{17}{2}\right){x}+\frac{3}{4}a^{3}+\frac{1}{2}a^{2}-\frac{19}{2}a-\frac{65}{4}$
20.2-c4 20.2-c 4.4.13025.1 \( 2^{2} \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.095546568$ $834.2473587$ 2.793708320 \( -\frac{77277}{20} a^{3} - \frac{220363}{80} a^{2} + \frac{322221}{8} a + \frac{4890201}{80} \) \( \bigl[-\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{1}{2} a - \frac{25}{4}\) , \( -\frac{1}{2} a^{3} + 2 a^{2} + a - \frac{15}{2}\) , \( a + 1\) , \( -\frac{25}{4} a^{3} + \frac{37}{2} a^{2} + \frac{47}{2} a - \frac{253}{4}\) , \( -\frac{37}{4} a^{3} + \frac{59}{2} a^{2} + \frac{67}{2} a - \frac{417}{4}\bigr] \) ${y}^2+\left(-\frac{1}{4}a^{3}+\frac{3}{2}a^{2}+\frac{1}{2}a-\frac{25}{4}\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+2a^{2}+a-\frac{15}{2}\right){x}^{2}+\left(-\frac{25}{4}a^{3}+\frac{37}{2}a^{2}+\frac{47}{2}a-\frac{253}{4}\right){x}-\frac{37}{4}a^{3}+\frac{59}{2}a^{2}+\frac{67}{2}a-\frac{417}{4}$
20.2-d1 20.2-d 4.4.13025.1 \( 2^{2} \cdot 5 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.111243523$ $12.56817735$ 3.426499781 \( -\frac{11751267618729}{320} a^{3} + \frac{67868984066577}{640} a^{2} + \frac{7695614514961}{32} a - \frac{361053674523679}{640} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a^{2} - 6\) , \( \frac{131}{4} a^{3} + \frac{161}{2} a^{2} - \frac{813}{2} a - \frac{3949}{4}\) , \( \frac{1155}{2} a^{3} + 779 a^{2} - 6428 a - \frac{23863}{2}\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(\frac{131}{4}a^{3}+\frac{161}{2}a^{2}-\frac{813}{2}a-\frac{3949}{4}\right){x}+\frac{1155}{2}a^{3}+779a^{2}-6428a-\frac{23863}{2}$
20.4-a1 20.4-a 4.4.13025.1 \( 2^{2} \cdot 5 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $236.3617268$ 2.071039052 \( -\frac{9401109}{500} a^{3} + 73488 a^{2} + \frac{6875922}{125} a - \frac{142950859}{500} \) \( \bigl[-\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{3}{2} a - \frac{25}{4}\) , \( -\frac{1}{2} a^{3} + 2 a^{2} + 3 a - \frac{19}{2}\) , \( -\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{3}{2} a - \frac{29}{4}\) , \( \frac{11}{4} a^{3} - \frac{7}{2} a^{2} - \frac{15}{2} a + \frac{35}{4}\) , \( -\frac{3}{2} a^{3} + 18 a^{2} + 9 a - \frac{133}{2}\bigr] \) ${y}^2+\left(-\frac{1}{4}a^{3}+\frac{3}{2}a^{2}+\frac{3}{2}a-\frac{25}{4}\right){x}{y}+\left(-\frac{1}{4}a^{3}+\frac{3}{2}a^{2}+\frac{3}{2}a-\frac{29}{4}\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+2a^{2}+3a-\frac{19}{2}\right){x}^{2}+\left(\frac{11}{4}a^{3}-\frac{7}{2}a^{2}-\frac{15}{2}a+\frac{35}{4}\right){x}-\frac{3}{2}a^{3}+18a^{2}+9a-\frac{133}{2}$
20.4-a2 20.4-a 4.4.13025.1 \( 2^{2} \cdot 5 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $236.3617268$ 2.071039052 \( -\frac{162115029}{320} a^{3} + 1734307 a^{2} + \frac{74863321}{40} a - \frac{1937758859}{320} \) \( \bigl[a^{2} - a - 5\) , \( -a^{2} + 5\) , \( -\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{3}{2} a - \frac{29}{4}\) , \( -\frac{45}{4} a^{3} + \frac{49}{2} a^{2} + \frac{163}{2} a - \frac{433}{4}\) , \( \frac{205}{2} a^{3} - 356 a^{2} - 608 a + \frac{4161}{2}\bigr] \) ${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(-\frac{1}{4}a^{3}+\frac{3}{2}a^{2}+\frac{3}{2}a-\frac{29}{4}\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-\frac{45}{4}a^{3}+\frac{49}{2}a^{2}+\frac{163}{2}a-\frac{433}{4}\right){x}+\frac{205}{2}a^{3}-356a^{2}-608a+\frac{4161}{2}$
20.4-b1 20.4-b 4.4.13025.1 \( 2^{2} \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.081102252$ $435.4459260$ 3.094413023 \( -\frac{3499622813}{8000} a^{3} - \frac{517230431}{800} a^{2} + \frac{19714845153}{4000} a + \frac{76143159447}{8000} \) \( \bigl[-\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{3}{2} a - \frac{29}{4}\) , \( a\) , \( a\) , \( 3 a^{2} + 4 a - 15\) , \( -\frac{3}{4} a^{3} + \frac{17}{2} a^{2} + \frac{13}{2} a - \frac{143}{4}\bigr] \) ${y}^2+\left(-\frac{1}{4}a^{3}+\frac{3}{2}a^{2}+\frac{3}{2}a-\frac{29}{4}\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(3a^{2}+4a-15\right){x}-\frac{3}{4}a^{3}+\frac{17}{2}a^{2}+\frac{13}{2}a-\frac{143}{4}$
20.4-b2 20.4-b 4.4.13025.1 \( 2^{2} \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.162204504$ $435.4459260$ 3.094413023 \( -\frac{61013391}{10000} a^{3} + \frac{511672137}{25000} a^{2} + \frac{580208277}{25000} a - \frac{3413113859}{50000} \) \( \bigl[-\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{3}{2} a - \frac{29}{4}\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a + \frac{5}{4}\) , \( 1\) , \( \frac{1}{4} a^{3} + \frac{15}{2} a^{2} - \frac{19}{2} a - \frac{255}{4}\) , \( -\frac{53}{4} a^{3} + \frac{23}{2} a^{2} + \frac{233}{2} a + \frac{103}{4}\bigr] \) ${y}^2+\left(-\frac{1}{4}a^{3}+\frac{3}{2}a^{2}+\frac{3}{2}a-\frac{29}{4}\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{1}{2}a^{2}-\frac{5}{2}a+\frac{5}{4}\right){x}^{2}+\left(\frac{1}{4}a^{3}+\frac{15}{2}a^{2}-\frac{19}{2}a-\frac{255}{4}\right){x}-\frac{53}{4}a^{3}+\frac{23}{2}a^{2}+\frac{233}{2}a+\frac{103}{4}$
20.4-b3 20.4-b 4.4.13025.1 \( 2^{2} \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.324409008$ $217.7229630$ 3.094413023 \( -\frac{499606195539}{1000} a^{3} + \frac{171117825807}{100} a^{2} + \frac{922843609059}{500} a - \frac{5974683178759}{1000} \) \( \bigl[a^{2} - 6\) , \( a^{2} - a - 7\) , \( -\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{3}{2} a - \frac{25}{4}\) , \( -8 a^{2} + a + 28\) , \( \frac{17}{4} a^{3} - \frac{23}{2} a^{2} - \frac{31}{2} a + \frac{157}{4}\bigr] \) ${y}^2+\left(a^{2}-6\right){x}{y}+\left(-\frac{1}{4}a^{3}+\frac{3}{2}a^{2}+\frac{3}{2}a-\frac{25}{4}\right){y}={x}^{3}+\left(a^{2}-a-7\right){x}^{2}+\left(-8a^{2}+a+28\right){x}+\frac{17}{4}a^{3}-\frac{23}{2}a^{2}-\frac{31}{2}a+\frac{157}{4}$
20.4-b4 20.4-b 4.4.13025.1 \( 2^{2} \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.324409008$ $54.43074075$ 3.094413023 \( \frac{1405180548839}{78125000} a^{3} - \frac{324597888071}{39062500} a^{2} - \frac{141699152679}{1562500} a + \frac{6675478129771}{78125000} \) \( \bigl[a\) , \( -\frac{1}{2} a^{3} + 2 a^{2} + a - \frac{19}{2}\) , \( -\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{1}{2} a - \frac{25}{4}\) , \( -\frac{161}{4} a^{3} - \frac{19}{2} a^{2} + \frac{787}{2} a + \frac{1863}{4}\) , \( -\frac{2077}{4} a^{3} - \frac{895}{2} a^{2} + \frac{11003}{2} a + \frac{34335}{4}\bigr] \) ${y}^2+a{x}{y}+\left(-\frac{1}{4}a^{3}+\frac{3}{2}a^{2}+\frac{1}{2}a-\frac{25}{4}\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+2a^{2}+a-\frac{19}{2}\right){x}^{2}+\left(-\frac{161}{4}a^{3}-\frac{19}{2}a^{2}+\frac{787}{2}a+\frac{1863}{4}\right){x}-\frac{2077}{4}a^{3}-\frac{895}{2}a^{2}+\frac{11003}{2}a+\frac{34335}{4}$
20.4-c1 20.4-c 4.4.13025.1 \( 2^{2} \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.095546568$ $834.2473587$ 2.793708320 \( -\frac{2384607}{320} a^{3} + \frac{812353}{32} a^{2} + \frac{4418697}{160} a - \frac{27670247}{320} \) \( \bigl[-\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{1}{2} a - \frac{29}{4}\) , \( a^{2} - 7\) , \( a^{2} - a - 5\) , \( -\frac{1}{2} a^{3} + 3 a^{2} + 4 a - \frac{39}{2}\) , \( a^{3} - 2 a^{2} - 6 a + 9\bigr] \) ${y}^2+\left(-\frac{1}{4}a^{3}+\frac{3}{2}a^{2}+\frac{1}{2}a-\frac{29}{4}\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a^{2}-7\right){x}^{2}+\left(-\frac{1}{2}a^{3}+3a^{2}+4a-\frac{39}{2}\right){x}+a^{3}-2a^{2}-6a+9$
20.4-c2 20.4-c 4.4.13025.1 \( 2^{2} \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.382186275$ $417.1236793$ 2.793708320 \( \frac{34683}{40} a^{3} + \frac{285619}{100} a^{2} - \frac{273201}{100} a - \frac{1901033}{200} \) \( \bigl[-\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{1}{2} a - \frac{25}{4}\) , \( -\frac{1}{2} a^{3} + 2 a^{2} + 3 a - \frac{17}{2}\) , \( -\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{3}{2} a - \frac{29}{4}\) , \( -\frac{5}{4} a^{3} + \frac{11}{2} a^{2} + \frac{7}{2} a - \frac{69}{4}\) , \( -\frac{9}{4} a^{3} + \frac{17}{2} a^{2} + \frac{17}{2} a - \frac{133}{4}\bigr] \) ${y}^2+\left(-\frac{1}{4}a^{3}+\frac{3}{2}a^{2}+\frac{1}{2}a-\frac{25}{4}\right){x}{y}+\left(-\frac{1}{4}a^{3}+\frac{3}{2}a^{2}+\frac{3}{2}a-\frac{29}{4}\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+2a^{2}+3a-\frac{17}{2}\right){x}^{2}+\left(-\frac{5}{4}a^{3}+\frac{11}{2}a^{2}+\frac{7}{2}a-\frac{69}{4}\right){x}-\frac{9}{4}a^{3}+\frac{17}{2}a^{2}+\frac{17}{2}a-\frac{133}{4}$
20.4-c3 20.4-c 4.4.13025.1 \( 2^{2} \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.191093137$ $1668.494717$ 2.793708320 \( \frac{490359}{80} a^{3} - \frac{980423}{40} a^{2} - \frac{1308507}{40} a + \frac{2466303}{16} \) \( \bigl[-\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{1}{2} a - \frac{25}{4}\) , \( -\frac{1}{4} a^{3} + \frac{1}{2} a^{2} + \frac{3}{2} a - \frac{5}{4}\) , \( a^{2} - 5\) , \( -2 a^{2} + 7\) , \( \frac{7}{4} a^{3} - \frac{15}{2} a^{2} - \frac{13}{2} a + \frac{103}{4}\bigr] \) ${y}^2+\left(-\frac{1}{4}a^{3}+\frac{3}{2}a^{2}+\frac{1}{2}a-\frac{25}{4}\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}+\frac{1}{2}a^{2}+\frac{3}{2}a-\frac{5}{4}\right){x}^{2}+\left(-2a^{2}+7\right){x}+\frac{7}{4}a^{3}-\frac{15}{2}a^{2}-\frac{13}{2}a+\frac{103}{4}$
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  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.