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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
2.1-a1 2.1-a 3.3.940.1 \( 2 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.009848962$ $265.3922715$ 0.511524064 \( -\frac{1897}{4} a^{2} - 353 a + \frac{6735}{4} \) \( \bigl[a^{2} - 5\) , \( a^{2} - a - 5\) , \( a\) , \( -2 a - 2\) , \( 0\bigr] \) ${y}^2+\left(a^{2}-5\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-2a-2\right){x}$
2.1-a2 2.1-a 3.3.940.1 \( 2 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.049244811$ $53.07845431$ 0.511524064 \( \frac{947071607}{1024} a^{2} - \frac{142177921}{256} a - \frac{6291555537}{1024} \) \( \bigl[a^{2} - 5\) , \( 1\) , \( a^{2} - 4\) , \( -36 a^{2} + 83 a + 59\) , \( -284 a^{2} + 651 a + 493\bigr] \) ${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+{x}^{2}+\left(-36a^{2}+83a+59\right){x}-284a^{2}+651a+493$
4.1-a1 4.1-a 3.3.940.1 \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $25.56327504$ 2.084455243 \( \frac{5682805}{32} a^{2} + \frac{17340215}{32} a + \frac{8387901}{32} \) \( \bigl[a^{2} - a - 5\) , \( a^{2} - a - 4\) , \( a + 1\) , \( -47 a^{2} + 107 a + 84\) , \( -466 a^{2} + 1066 a + 816\bigr] \) ${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-47a^{2}+107a+84\right){x}-466a^{2}+1066a+816$
4.1-a2 4.1-a 3.3.940.1 \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $127.8163752$ 2.084455243 \( -\frac{398753577}{4} a^{2} + \frac{120161319}{2} a + \frac{2646449161}{4} \) \( \bigl[a^{2} - a - 5\) , \( a - 1\) , \( 0\) , \( -117 a^{2} + 268 a + 206\) , \( 1378 a^{2} - 3159 a - 2404\bigr] \) ${y}^2+\left(a^{2}-a-5\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-117a^{2}+268a+206\right){x}+1378a^{2}-3159a-2404$
4.1-a3 4.1-a 3.3.940.1 \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $127.8163752$ 2.084455243 \( \frac{64525}{2} a^{2} + \frac{158775}{2} a + \frac{25181}{2} \) \( \bigl[1\) , \( a^{2} - a - 4\) , \( a^{2} - 5\) , \( -2 a^{2} - 6 a + 2\) , \( 4 a^{2} + 6 a - 4\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-2a^{2}-6a+2\right){x}+4a^{2}+6a-4$
4.1-a4 4.1-a 3.3.940.1 \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $25.56327504$ 2.084455243 \( \frac{264544214121}{1024} a^{2} - \frac{151611822399}{256} a - \frac{461586534863}{1024} \) \( \bigl[1\) , \( a^{2} - 4\) , \( 1\) , \( -105115 a^{2} + 240969 a + 183412\) , \( -38888874 a^{2} + 89148913 a + 67857014\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-105115a^{2}+240969a+183412\right){x}-38888874a^{2}+89148913a+67857014$
5.1-a1 5.1-a 3.3.940.1 \( 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $183.1922990$ 1.493768493 \( -\frac{8468}{5} a^{2} + \frac{4144}{5} a + \frac{57849}{5} \) \( \bigl[a^{2} - a - 5\) , \( -a\) , \( a^{2} - 5\) , \( -a^{2} - 7 a - 6\) , \( 16 a^{2} + 44 a + 19\bigr] \) ${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}-a{x}^{2}+\left(-a^{2}-7a-6\right){x}+16a^{2}+44a+19$
5.1-a2 5.1-a 3.3.940.1 \( 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $183.1922990$ 1.493768493 \( -\frac{20786237}{5} a^{2} + \frac{5310351}{5} a + \frac{158857721}{5} \) \( \bigl[a^{2} - a - 5\) , \( -a^{2} + 2 a + 4\) , \( a + 1\) , \( -1533 a^{2} + 3510 a + 2687\) , \( -66131 a^{2} + 151595 a + 115399\bigr] \) ${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(-1533a^{2}+3510a+2687\right){x}-66131a^{2}+151595a+115399$
5.1-a3 5.1-a 3.3.940.1 \( 5 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $366.3845981$ 1.493768493 \( \frac{148422}{5} a^{2} + \frac{437592}{5} a + \frac{240941}{5} \) \( \bigl[1\) , \( -a^{2} + a + 4\) , \( 1\) , \( -a^{2} + a + 4\) , \( 1\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-a^{2}+a+4\right){x}+1$
5.1-a4 5.1-a 3.3.940.1 \( 5 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $183.1922990$ 1.493768493 \( \frac{416211993101}{25} a^{2} + \frac{1204977729061}{25} a + \frac{575055675183}{25} \) \( \bigl[1\) , \( -a^{2} + a + 4\) , \( 1\) , \( -6 a^{2} + 6 a + 9\) , \( 18 a^{2} - 26 a - 21\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-6a^{2}+6a+9\right){x}+18a^{2}-26a-21$
5.2-a1 5.2-a 3.3.940.1 \( 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $20.50717563$ 0.668870318 \( -\frac{199332986876}{5} a^{2} + \frac{120136663044}{5} a + \frac{1322930343681}{5} \) \( \bigl[a^{2} - a - 5\) , \( -a - 1\) , \( 1\) , \( 106 a^{2} - 63 a - 702\) , \( 1165 a^{2} - 702 a - 7734\bigr] \) ${y}^2+\left(a^{2}-a-5\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(106a^{2}-63a-702\right){x}+1165a^{2}-702a-7734$
5.2-a2 5.2-a 3.3.940.1 \( 5 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $164.0574050$ 0.668870318 \( -\frac{2046904}{25} a^{2} + \frac{1230056}{25} a + \frac{13638769}{25} \) \( \bigl[a^{2} - a - 5\) , \( -a - 1\) , \( 1\) , \( 6 a^{2} - 3 a - 37\) , \( 24 a^{2} - 15 a - 160\bigr] \) ${y}^2+\left(a^{2}-a-5\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(6a^{2}-3a-37\right){x}+24a^{2}-15a-160$
5.2-a3 5.2-a 3.3.940.1 \( 5 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $164.0574050$ 0.668870318 \( \frac{197192105429}{25} a^{2} + \frac{570892174269}{25} a + \frac{272448900581}{25} \) \( \bigl[a^{2} - a - 5\) , \( -a^{2} + a + 6\) , \( a^{2} - 4\) , \( 225 a^{2} - 526 a - 364\) , \( 392426 a^{2} - 899618 a - 684689\bigr] \) ${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(225a^{2}-526a-364\right){x}+392426a^{2}-899618a-684689$
5.2-a4 5.2-a 3.3.940.1 \( 5 \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $328.1148101$ 0.668870318 \( \frac{16042346}{625} a^{2} + \frac{30639556}{625} a + \frac{13745569}{625} \) \( \bigl[1\) , \( a - 1\) , \( a^{2} - a - 5\) , \( -15 a^{2} + 38 a + 17\) , \( 97 a^{2} - 222 a - 170\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-15a^{2}+38a+17\right){x}+97a^{2}-222a-170$
5.2-a5 5.2-a 3.3.940.1 \( 5 \) 0 $\Z/8\Z$ $\mathrm{SU}(2)$ $1$ $164.0574050$ 0.668870318 \( \frac{85288749659771}{390625} a^{2} - \frac{195535485731269}{390625} a - \frac{148763739022981}{390625} \) \( \bigl[1\) , \( a - 1\) , \( a^{2} - a - 5\) , \( -250 a^{2} + 613 a + 322\) , \( 5318 a^{2} - 12391 a - 8700\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-250a^{2}+613a+322\right){x}+5318a^{2}-12391a-8700$
5.2-a6 5.2-a 3.3.940.1 \( 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $82.02870253$ 0.668870318 \( \frac{1306}{5} a^{2} - \frac{264}{5} a - \frac{1601}{5} \) \( \bigl[1\) , \( -a^{2} + a + 6\) , \( a\) , \( a + 4\) , \( 4 a^{2} - 2 a - 27\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(a+4\right){x}+4a^{2}-2a-27$
8.1-a1 8.1-a 3.3.940.1 \( 2^{3} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $116.1061059$ 0.946740904 \( -\frac{411926287272281}{128} a^{2} + \frac{62067501092911}{32} a + \frac{2733850455242975}{128} \) \( \bigl[a^{2} - 5\) , \( -a^{2} + 2 a + 4\) , \( a^{2} - 5\) , \( 513 a^{2} - 316 a - 3409\) , \( -9574 a^{2} + 5824 a + 63656\bigr] \) ${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(513a^{2}-316a-3409\right){x}-9574a^{2}+5824a+63656$
8.1-a2 8.1-a 3.3.940.1 \( 2^{3} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $116.1061059$ 0.946740904 \( \frac{31029133791577}{128} a^{2} - \frac{17449377850799}{32} a - \frac{53338737080543}{128} \) \( \bigl[a + 1\) , \( -1\) , \( a^{2} - a - 4\) , \( 6039 a^{2} - 3631 a - 40105\) , \( -283676 a^{2} + 170947 a + 1882761\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}-{x}^{2}+\left(6039a^{2}-3631a-40105\right){x}-283676a^{2}+170947a+1882761$
8.1-a3 8.1-a 3.3.940.1 \( 2^{3} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $232.2122118$ 0.946740904 \( -\frac{9204129895}{16384} a^{2} + \frac{391390225}{4096} a + \frac{75753312097}{16384} \) \( \bigl[a + 1\) , \( -1\) , \( a^{2} - a - 4\) , \( 5419 a^{2} - 3266 a - 35965\) , \( -374961 a^{2} + 225991 a + 2488521\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}-{x}^{2}+\left(5419a^{2}-3266a-35965\right){x}-374961a^{2}+225991a+2488521$
8.1-a4 8.1-a 3.3.940.1 \( 2^{3} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $58.05305296$ 0.946740904 \( \frac{72406586393}{268435456} a^{2} + \frac{19685037201}{67108864} a - \frac{363726133279}{268435456} \) \( \bigl[a + 1\) , \( -a\) , \( a^{2} - 5\) , \( 1221 a^{2} - 674 a - 8289\) , \( -61314 a^{2} + 36140 a + 409280\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}-a{x}^{2}+\left(1221a^{2}-674a-8289\right){x}-61314a^{2}+36140a+409280$
8.1-b1 8.1-b 3.3.940.1 \( 2^{3} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.706913567$ 1.002120874 \( -\frac{4506419129977}{64} a^{2} + \frac{2582846188559}{16} a + \frac{7860731202239}{64} \) \( \bigl[a^{2} - 5\) , \( -a^{2} + 6\) , \( a + 1\) , \( 58 a^{2} - 37 a - 391\) , \( 732 a^{2} - 443 a - 4864\bigr] \) ${y}^2+\left(a^{2}-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(58a^{2}-37a-391\right){x}+732a^{2}-443a-4864$
8.1-b2 8.1-b 3.3.940.1 \( 2^{3} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $46.08666632$ 1.002120874 \( -\frac{3289}{4} a^{2} + 2223 a + \frac{6495}{4} \) \( \bigl[a^{2} - 5\) , \( -a^{2} + 6\) , \( a + 1\) , \( -7 a^{2} + 3 a + 44\) , \( -6 a^{2} + 3 a + 38\bigr] \) ${y}^2+\left(a^{2}-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(-7a^{2}+3a+44\right){x}-6a^{2}+3a+38$
8.2-a1 8.2-a 3.3.940.1 \( 2^{3} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.007144739$ $58.16900756$ 2.805979536 \( \frac{757971727}{4096} a^{2} - \frac{456662163}{4096} a - \frac{1257523137}{1024} \) \( \bigl[a\) , \( a\) , \( a\) , \( 2 a - 1\) , \( 5 a^{2} - 11 a - 7\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(2a-1\right){x}+5a^{2}-11a-7$
8.2-b1 8.2-b 3.3.940.1 \( 2^{3} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $2.425628142$ 0.712037399 \( -\frac{85276761673}{131072} a^{2} - \frac{246981661297}{131072} a - \frac{29512153075}{32768} \) \( \bigl[a\) , \( a + 1\) , \( a\) , \( -5 a^{2} - 18 a - 18\) , \( -38 a^{2} - 119 a - 75\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-5a^{2}-18a-18\right){x}-38a^{2}-119a-75$
8.2-b2 8.2-b 3.3.940.1 \( 2^{3} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $65.49195985$ 0.712037399 \( -\frac{8729}{64} a^{2} + \frac{4725}{64} a + \frac{14871}{16} \) \( \bigl[a\) , \( a + 1\) , \( a\) , \( 2 a + 2\) , \( a + 1\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a+2\right){x}+a+1$
8.4-a1 8.4-a 3.3.940.1 \( 2^{3} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $15.69521707$ 1.023843070 \( -14596 a^{2} + 34928 a + 21212 \) \( \bigl[0\) , \( -a\) , \( a^{2} - 4\) , \( 2 a - 3\) , \( -a^{2} + 3 a - 6\bigr] \) ${y}^2+\left(a^{2}-4\right){y}={x}^{3}-a{x}^{2}+\left(2a-3\right){x}-a^{2}+3a-6$
10.2-a1 10.2-a 3.3.940.1 \( 2 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.173638506$ $87.03496867$ 1.478758139 \( \frac{1176761}{100} a^{2} + \frac{847874}{25} a + \frac{1736929}{100} \) \( \bigl[a^{2} - a - 5\) , \( -a^{2} + 2 a + 5\) , \( a^{2} - 4\) , \( 13396 a^{2} - 30712 a - 23365\) , \( -767129 a^{2} + 1758563 a + 1338569\bigr] \) ${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+2a+5\right){x}^{2}+\left(13396a^{2}-30712a-23365\right){x}-767129a^{2}+1758563a+1338569$
10.2-a2 10.2-a 3.3.940.1 \( 2 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.347277013$ $174.0699373$ 1.478758139 \( -\frac{1831}{10} a^{2} - \frac{1458}{5} a + \frac{23271}{10} \) \( \bigl[1\) , \( -a - 1\) , \( a^{2} - 4\) , \( -27 a^{2} + 62 a + 49\) , \( -75 a^{2} + 171 a + 127\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-27a^{2}+62a+49\right){x}-75a^{2}+171a+127$
10.2-b1 10.2-b 3.3.940.1 \( 2 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.309868878$ $33.61809242$ 1.019314858 \( -\frac{7820493189972621}{10000000000} a^{2} + \frac{1180705834842011}{2500000000} a + \frac{51924634646264331}{10000000000} \) \( \bigl[a + 1\) , \( a^{2} - 5\) , \( a^{2} - 4\) , \( 277223 a^{2} - 167091 a - 1839829\) , \( -136978402 a^{2} + 82557689 a + 909090597\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(277223a^{2}-167091a-1839829\right){x}-136978402a^{2}+82557689a+909090597$
10.2-b2 10.2-b 3.3.940.1 \( 2 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.061973775$ $168.0904621$ 1.019314858 \( \frac{109681793539}{100} a^{2} + \frac{79391233451}{25} a + \frac{151594310171}{100} \) \( \bigl[a + 1\) , \( a\) , \( a^{2} - a - 5\) , \( 306 a^{2} - 182 a - 2024\) , \( 4923 a^{2} - 2965 a - 32668\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+a{x}^{2}+\left(306a^{2}-182a-2024\right){x}+4923a^{2}-2965a-32668$
10.2-b3 10.2-b 3.3.940.1 \( 2 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.619737756$ $33.61809242$ 1.019314858 \( \frac{6982054663829}{3276800000} a^{2} - \frac{3534620649939}{819200000} a - \frac{15950242311619}{3276800000} \) \( \bigl[a + 1\) , \( 1\) , \( a\) , \( 365 a^{2} - 188 a - 2513\) , \( -10291 a^{2} + 6364 a + 67833\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(365a^{2}-188a-2513\right){x}-10291a^{2}+6364a+67833$
10.2-b4 10.2-b 3.3.940.1 \( 2 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.123947551$ $168.0904621$ 1.019314858 \( \frac{7035191109}{80} a^{2} - \frac{4032672419}{20} a - \frac{12277613459}{80} \) \( \bigl[a + 1\) , \( -a^{2} + 5\) , \( a^{2} - 4\) , \( -2 a^{2} + 7\) , \( a^{2} - 2 a - 7\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-2a^{2}+7\right){x}+a^{2}-2a-7$
10.3-a1 10.3-a 3.3.940.1 \( 2 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $33.32566605$ 1.630445064 \( \frac{23720555509601}{400} a^{2} + \frac{17168383605253}{100} a + \frac{32773310108297}{400} \) \( \bigl[a^{2} - a - 5\) , \( a - 1\) , \( a^{2} - 4\) , \( -28818 a^{2} + 66064 a + 50280\) , \( -4032774 a^{2} + 9244737 a + 7036764\bigr] \) ${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-28818a^{2}+66064a+50280\right){x}-4032774a^{2}+9244737a+7036764$
10.3-a2 10.3-a 3.3.940.1 \( 2 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $66.65133211$ 1.630445064 \( \frac{2403467803}{50} a^{2} - \frac{2754859882}{25} a - \frac{4193802859}{50} \) \( \bigl[a^{2} - a - 5\) , \( 1\) , \( 0\) , \( -4 a^{2} - 5 a + 7\) , \( -14 a^{2} - 38 a - 13\bigr] \) ${y}^2+\left(a^{2}-a-5\right){x}{y}={x}^{3}+{x}^{2}+\left(-4a^{2}-5a+7\right){x}-14a^{2}-38a-13$
10.3-a3 10.3-a 3.3.940.1 \( 2 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $16.66283302$ 1.630445064 \( -\frac{8249041263949}{6250} a^{2} + \frac{12429350495779}{15625} a + \frac{273734017379507}{31250} \) \( \bigl[1\) , \( a^{2} - a - 4\) , \( a^{2} - a - 5\) , \( 43 a^{2} - 100 a - 72\) , \( 2869 a^{2} - 6576 a - 5010\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(43a^{2}-100a-72\right){x}+2869a^{2}-6576a-5010$
10.3-a4 10.3-a 3.3.940.1 \( 2 \cdot 5 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $66.65133211$ 1.630445064 \( \frac{22283521}{500} a^{2} + \frac{845721}{5} a + \frac{87411109}{500} \) \( \bigl[1\) , \( a^{2} - a - 4\) , \( a^{2} - a - 5\) , \( -77 a^{2} + 175 a + 138\) , \( 636 a^{2} - 1457 a - 1114\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-77a^{2}+175a+138\right){x}+636a^{2}-1457a-1114$
10.3-b1 10.3-b 3.3.940.1 \( 2 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.343736707$ $88.77942622$ 1.493019839 \( -\frac{193827}{16000} a^{2} + \frac{5771573}{4000} a + \frac{5261121}{3200} \) \( \bigl[a^{2} - a - 5\) , \( a^{2} - a - 4\) , \( 1\) , \( -651 a^{2} + 391 a + 4325\) , \( -17579 a^{2} + 10594 a + 116670\bigr] \) ${y}^2+\left(a^{2}-a-5\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-651a^{2}+391a+4325\right){x}-17579a^{2}+10594a+116670$
10.3-b2 10.3-b 3.3.940.1 \( 2 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.171868353$ $177.5588524$ 1.493019839 \( \frac{267566946241}{409600} a^{2} - \frac{153109164807}{102400} a - \frac{464857186103}{409600} \) \( \bigl[1\) , \( a^{2} - a - 6\) , \( 1\) , \( -14 a^{2} - 37 a - 11\) , \( 72 a^{2} + 207 a + 96\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(-14a^{2}-37a-11\right){x}+72a^{2}+207a+96$
10.4-a1 10.4-a 3.3.940.1 \( 2 \cdot 5 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $30.40009460$ 4.957708782 \( -\frac{61275099}{25000} a^{2} - \frac{180652339}{25000} a - \frac{23030009}{6250} \) \( \bigl[a^{2} - 4\) , \( 1\) , \( 1\) , \( 627 a^{2} - 1437 a - 1086\) , \( -4844453 a^{2} + 11105433 a + 8453065\bigr] \) ${y}^2+\left(a^{2}-4\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(627a^{2}-1437a-1086\right){x}-4844453a^{2}+11105433a+8453065$
10.4-a2 10.4-a 3.3.940.1 \( 2 \cdot 5 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $152.0004730$ 4.957708782 \( -\frac{7961}{10} a^{2} + \frac{21879}{10} a + \frac{2378}{5} \) \( \bigl[a\) , \( -a^{2} + 2 a + 4\) , \( a^{2} - a - 5\) , \( -213 a^{2} + 489 a + 373\) , \( 4232 a^{2} - 9700 a - 7387\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(-213a^{2}+489a+373\right){x}+4232a^{2}-9700a-7387$
16.1-a1 16.1-a 3.3.940.1 \( 2^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.065519200$ $142.6219394$ 2.743048637 \( 176 a^{2} + 192 a - 464 \) \( \bigl[0\) , \( a^{2} - 4\) , \( a^{2} - a - 4\) , \( a + 5\) , \( 2 a^{2} - 2 a - 6\bigr] \) ${y}^2+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(a+5\right){x}+2a^{2}-2a-6$
16.3-a1 16.3-a 3.3.940.1 \( 2^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.020911567$ $250.9796113$ 2.054198191 \( -\frac{357289}{64} a^{2} + \frac{160863}{16} a + \frac{560143}{64} \) \( \bigl[a^{2} - 5\) , \( a^{2} - 2 a - 6\) , \( a + 1\) , \( -a^{2} - a + 1\) , \( 0\bigr] \) ${y}^2+\left(a^{2}-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2a-6\right){x}^{2}+\left(-a^{2}-a+1\right){x}$
16.3-b1 16.3-b 3.3.940.1 \( 2^{4} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $104.4171066$ 2.554282874 \( -\frac{14358055}{4096} a^{2} + \frac{1931345}{1024} a + \frac{102398881}{4096} \) \( \bigl[a + 1\) , \( a^{2} - 2 a - 5\) , \( a^{2} - 5\) , \( -116019 a^{2} + 265977 a + 202392\) , \( 21568154 a^{2} - 49442942 a - 37633959\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(-116019a^{2}+265977a+202392\right){x}+21568154a^{2}-49442942a-37633959$
16.3-b2 16.3-b 3.3.940.1 \( 2^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $52.20855334$ 2.554282874 \( \frac{15529}{8} a^{2} + \frac{12161}{2} a + \frac{29905}{8} \) \( \bigl[a + 1\) , \( -a\) , \( a^{2} - a - 4\) , \( -4 a^{2} + a + 28\) , \( 8 a^{2} - 4 a - 56\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}-a{x}^{2}+\left(-4a^{2}+a+28\right){x}+8a^{2}-4a-56$
16.3-b3 16.3-b 3.3.940.1 \( 2^{4} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $104.4171066$ 2.554282874 \( \frac{392825}{64} a^{2} - \frac{228975}{16} a - \frac{469183}{64} \) \( \bigl[a + 1\) , \( -a^{2} + a + 6\) , \( a^{2} - a - 4\) , \( -411 a^{2} + 952 a + 692\) , \( -9369 a^{2} + 21517 a + 16236\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(-411a^{2}+952a+692\right){x}-9369a^{2}+21517a+16236$
16.3-b4 16.3-b 3.3.940.1 \( 2^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $26.10427667$ 2.554282874 \( \frac{2955149311}{8} a^{2} - \frac{1695875071}{2} a - \frac{5103413233}{8} \) \( \bigl[a + 1\) , \( -a^{2} + a + 6\) , \( a^{2} - a - 4\) , \( -6541 a^{2} + 15162 a + 10932\) , \( -612967 a^{2} + 1407035 a + 1064156\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(-6541a^{2}+15162a+10932\right){x}-612967a^{2}+1407035a+1064156$
16.4-a1 16.4-a 3.3.940.1 \( 2^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $28.03962680$ 1.829103572 \( -\frac{55372771}{2} a^{2} + \frac{126939965}{2} a + 48304494 \) \( \bigl[a^{2} - 4\) , \( 0\) , \( a\) , \( 3 a^{2} - 2 a - 19\) , \( -3 a^{2} + 2 a + 19\bigr] \) ${y}^2+\left(a^{2}-4\right){x}{y}+a{y}={x}^{3}+\left(3a^{2}-2a-19\right){x}-3a^{2}+2a+19$
16.4-b1 16.4-b 3.3.940.1 \( 2^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.020684313$ $275.8143528$ 3.349396386 \( -\frac{665}{4} a^{2} - \frac{1931}{4} a - 233 \) \( \bigl[a\) , \( a^{2} - a - 4\) , \( 0\) , \( -3 a + 1\) , \( a^{2} - 1\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-3a+1\right){x}+a^{2}-1$
16.4-c1 16.4-c 3.3.940.1 \( 2^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.028098905$ $297.5924836$ 1.636434724 \( \frac{46477839}{16} a^{2} - \frac{28086419}{16} a - \frac{77159361}{4} \) \( \bigl[a^{2} - 4\) , \( a + 1\) , \( a\) , \( -a^{2} - 3 a\) , \( a + 1\bigr] \) ${y}^2+\left(a^{2}-4\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-a^{2}-3a\right){x}+a+1$
16.4-d1 16.4-d 3.3.940.1 \( 2^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $27.71711614$ 0.904032648 \( -\frac{1869285816463}{4} a^{2} + \frac{1148471734001}{4} a + 3114012934081 \) \( \bigl[a^{2} - 4\) , \( -a - 1\) , \( a^{2} - 4\) , \( 9453243 a^{2} - 5697518 a - 62738784\) , \( 27206223747 a^{2} - 16397325199 a - 180560817484\bigr] \) ${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(9453243a^{2}-5697518a-62738784\right){x}+27206223747a^{2}-16397325199a-180560817484$
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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.