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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
1.1-a1 1.1-a 4.4.13968.1 \( 1 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $506.0694413$ 4.281963888 \( 2048 a^{2} - 2048 a - 16384 \) \( \bigl[0\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 3 a - 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( -4 a^{3} + \frac{15}{2} a^{2} + \frac{69}{2} a - 49\) , \( -17 a^{3} + 48 a^{2} + 67 a - 141\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+3a-1\right){x}^{2}+\left(-4a^{3}+\frac{15}{2}a^{2}+\frac{69}{2}a-49\right){x}-17a^{3}+48a^{2}+67a-141$
1.1-a2 1.1-a 4.4.13968.1 \( 1 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $506.0694413$ 4.281963888 \( -2269353142581248 a^{2} + 2269353142581248 a + 1216142683791360 \) \( \bigl[0\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( -202 a^{3} - \frac{535}{2} a^{2} + \frac{1125}{2} a + 282\) , \( 7126 a^{3} + \frac{17491}{2} a^{2} - \frac{40735}{2} a - 7572\bigr] \) ${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-4a\right){x}^{2}+\left(-202a^{3}-\frac{535}{2}a^{2}+\frac{1125}{2}a+282\right){x}+7126a^{3}+\frac{17491}{2}a^{2}-\frac{40735}{2}a-7572$
1.1-b1 1.1-b 4.4.13968.1 \( 1 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.364203461$ 0.288570573 \( -2269353142581248 a^{2} + 2269353142581248 a + 1216142683791360 \) \( \bigl[0\) , \( \frac{1}{2} a^{3} - \frac{9}{2} a - 2\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a\) , \( -2696 a^{3} + \frac{3293}{2} a^{2} + \frac{42289}{2} a + 7771\) , \( \frac{5442243}{2} a^{3} - \frac{3338845}{2} a^{2} - 21362570 a - 7850316\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{9}{2}a-2\right){x}^{2}+\left(-2696a^{3}+\frac{3293}{2}a^{2}+\frac{42289}{2}a+7771\right){x}+\frac{5442243}{2}a^{3}-\frac{3338845}{2}a^{2}-21362570a-7850316$
1.1-b2 1.1-b 4.4.13968.1 \( 1 \) 0 $\Z/5\Z$ $\mathrm{SU}(2)$ $1$ $852.6271632$ 0.288570573 \( 2048 a^{2} - 2048 a - 16384 \) \( \bigl[0\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a\) , \( -4 a^{3} + \frac{15}{2} a^{2} + \frac{69}{2} a - 49\) , \( 17 a^{3} - \frac{97}{2} a^{2} - \frac{137}{2} a + 139\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+1\right){x}^{2}+\left(-4a^{3}+\frac{15}{2}a^{2}+\frac{69}{2}a-49\right){x}+17a^{3}-\frac{97}{2}a^{2}-\frac{137}{2}a+139$
4.1-a1 4.1-a 4.4.13968.1 \( 2^{2} \) $1$ $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $0.090061613$ $626.2283084$ 1.908821413 \( 0 \) \( \bigl[0\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{3}{2} a - 2\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( a^{2} - 2 a + 1\) , \( -7 a^{3} + \frac{9}{2} a^{2} + \frac{103}{2} a + 18\bigr] \) ${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+a^{2}+\frac{3}{2}a-2\right){x}^{2}+\left(a^{2}-2a+1\right){x}-7a^{3}+\frac{9}{2}a^{2}+\frac{103}{2}a+18$
4.1-a2 4.1-a 4.4.13968.1 \( 2^{2} \) $1$ $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $0.030020537$ $626.2283084$ 1.908821413 \( 0 \) \( \bigl[0\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 2\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( a^{2} - 2 a + 1\) , \( \frac{13}{2} a^{3} - \frac{11}{2} a^{2} - 51 a - 18\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+2\right){x}^{2}+\left(a^{2}-2a+1\right){x}+\frac{13}{2}a^{3}-\frac{11}{2}a^{2}-51a-18$
4.2-a1 4.2-a 4.4.13968.1 \( 2^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $1222.405493$ 0.574613300 \( -\frac{282403}{16} a^{3} + \frac{1216941}{16} a^{2} - \frac{403623}{8} a - 28421 \) \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 1\) , \( -\frac{5}{2} a^{3} - 2 a^{2} + \frac{21}{2} a + 5\) , \( -\frac{3}{2} a^{3} - \frac{9}{2} a^{2} - 2 a\bigr] \) ${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}^{2}+\left(-\frac{5}{2}a^{3}-2a^{2}+\frac{21}{2}a+5\right){x}-\frac{3}{2}a^{3}-\frac{9}{2}a^{2}-2a$
4.2-a2 4.2-a 4.4.13968.1 \( 2^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $1222.405493$ 0.574613300 \( -\frac{16977046511811523}{2} a^{3} + \frac{145236159939106863}{4} a^{2} - \frac{93086123312290035}{4} a - \frac{29817939956784123}{2} \) \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 1\) , \( -130 a^{3} - 177 a^{2} + 338 a + 150\) , \( 3441 a^{3} + \frac{8919}{2} a^{2} - \frac{19019}{2} a - 4143\bigr] \) ${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}^{2}+\left(-130a^{3}-177a^{2}+338a+150\right){x}+3441a^{3}+\frac{8919}{2}a^{2}-\frac{19019}{2}a-4143$
4.2-a3 4.2-a 4.4.13968.1 \( 2^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $1222.405493$ 0.574613300 \( \frac{282403}{16} a^{3} + \frac{92433}{4} a^{2} - \frac{779427}{16} a - \frac{81861}{4} \) \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( -\frac{1}{2} a^{3} + \frac{7}{2} a\) , \( 0\) , \( \frac{5}{2} a^{3} - 10 a^{2} + \frac{11}{2} a + 11\) , \( -4 a^{3} + 14 a^{2} - a - 12\bigr] \) ${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){x}{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{7}{2}a\right){x}^{2}+\left(\frac{5}{2}a^{3}-10a^{2}+\frac{11}{2}a+11\right){x}-4a^{3}+14a^{2}-a-12$
4.2-a4 4.2-a 4.4.13968.1 \( 2^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $1222.405493$ 0.574613300 \( \frac{16977046511811523}{2} a^{3} + \frac{43373880868237725}{4} a^{2} - \frac{95523917495054553}{4} a - 10359984077593616 \) \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( -\frac{1}{2} a^{3} + \frac{7}{2} a\) , \( 0\) , \( 130 a^{3} - \frac{1135}{2} a^{2} + \frac{821}{2} a + 181\) , \( -\frac{7633}{2} a^{3} + \frac{32761}{2} a^{2} - 10724 a - 6446\bigr] \) ${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){x}{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{7}{2}a\right){x}^{2}+\left(130a^{3}-\frac{1135}{2}a^{2}+\frac{821}{2}a+181\right){x}-\frac{7633}{2}a^{3}+\frac{32761}{2}a^{2}-10724a-6446$
4.2-a5 4.2-a 4.4.13968.1 \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $15.09142584$ 0.574613300 \( -\frac{1533755475209}{1024} a^{3} + \frac{472673410411}{512} a^{2} + \frac{12028231718523}{1024} a + \frac{1104774680661}{256} \) \( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a\) , \( a + 1\) , \( -179 a^{3} - 230 a^{2} + 505 a + 219\) , \( -5998 a^{3} - 7664 a^{2} + 16873 a + 7320\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a\right){x}^{2}+\left(-179a^{3}-230a^{2}+505a+219\right){x}-5998a^{3}-7664a^{2}+16873a+7320$
4.2-a6 4.2-a 4.4.13968.1 \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $15.09142584$ 0.574613300 \( \frac{1533755475209}{1024} a^{3} - \frac{3655919604805}{1024} a^{2} - \frac{2329414733635}{256} a + \frac{3964730446695}{256} \) \( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a + 2\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( -\frac{135}{2} a^{3} + \frac{323}{2} a^{2} + 411 a - 730\) , \( -\frac{1619}{2} a^{3} + \frac{3905}{2} a^{2} + 4916 a - 8604\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a+2\right){x}^{2}+\left(-\frac{135}{2}a^{3}+\frac{323}{2}a^{2}+411a-730\right){x}-\frac{1619}{2}a^{3}+\frac{3905}{2}a^{2}+4916a-8604$
4.2-b1 4.2-b 4.4.13968.1 \( 2^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.921479734$ $595.0569893$ 2.319782351 \( 440995622435660464056 a^{3} + \frac{2253359137726065279771}{4} a^{2} - \frac{4962656994647070866229}{4} a - \frac{1076443444800172195515}{2} \) \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{3}{2} a - 2\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 1\) , \( -79 a^{3} - 97 a^{2} + 225 a + 85\) , \( 1733 a^{3} + 2194 a^{2} - 4890 a - 2057\bigr] \) ${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+a^{2}+\frac{3}{2}a-2\right){x}^{2}+\left(-79a^{3}-97a^{2}+225a+85\right){x}+1733a^{3}+2194a^{2}-4890a-2057$
4.2-b2 4.2-b 4.4.13968.1 \( 2^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.842959468$ $18.59553091$ 2.319782351 \( -440995622435660464056 a^{3} + \frac{7545306606953990848443}{4} a^{2} - \frac{4836008750032985261985}{4} a - 774550564194677030316 \) \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 2 a\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( \frac{381}{2} a^{3} - 114 a^{2} - \frac{2991}{2} a - 574\) , \( \frac{24299}{2} a^{3} - 7452 a^{2} - \frac{190751}{2} a - 35091\bigr] \) ${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+2a\right){x}^{2}+\left(\frac{381}{2}a^{3}-114a^{2}-\frac{2991}{2}a-574\right){x}+\frac{24299}{2}a^{3}-7452a^{2}-\frac{190751}{2}a-35091$
4.2-b3 4.2-b 4.4.13968.1 \( 2^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.307159911$ $297.5284946$ 2.319782351 \( \frac{26588277}{4} a^{3} - \frac{1015254405}{64} a^{2} - \frac{1292708889}{32} a + \frac{4403155923}{64} \) \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 2 a\) , \( 1\) , \( a^{3} - 2 a^{2} - 3 a\) , \( \frac{3}{2} a^{3} - 7 a^{2} + \frac{11}{2} a + 3\bigr] \) ${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+2a\right){x}^{2}+\left(a^{3}-2a^{2}-3a\right){x}+\frac{3}{2}a^{3}-7a^{2}+\frac{11}{2}a+3$
4.2-b4 4.2-b 4.4.13968.1 \( 2^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.614319822$ $18.59553091$ 2.319782351 \( \frac{8685450106503327}{16} a^{3} - 1295494095765510 a^{2} - \frac{52786626501280995}{16} a + \frac{22471527988464525}{4} \) \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 2 a\) , \( 1\) , \( 6 a^{3} - 37 a^{2} + 37 a + 20\) , \( \frac{135}{2} a^{3} - 317 a^{2} + \frac{499}{2} a + 147\bigr] \) ${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+2a\right){x}^{2}+\left(6a^{3}-37a^{2}+37a+20\right){x}+\frac{135}{2}a^{3}-317a^{2}+\frac{499}{2}a+147$
4.2-b5 4.2-b 4.4.13968.1 \( 2^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.842959468$ $74.38212366$ 2.319782351 \( -\frac{127972170891}{8} a^{3} + \frac{157018971825}{16} a^{2} + \frac{502330245489}{4} a + \frac{738385612533}{16} \) \( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 2 a - 2\) , \( 1\) , \( \frac{13}{2} a^{3} - 5 a^{2} - \frac{99}{2} a - 15\) , \( 31 a^{3} - 20 a^{2} - 240 a - 90\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+2a-2\right){x}^{2}+\left(\frac{13}{2}a^{3}-5a^{2}-\frac{99}{2}a-15\right){x}+31a^{3}-20a^{2}-240a-90$
4.2-b6 4.2-b 4.4.13968.1 \( 2^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.614319822$ $74.38212366$ 2.319782351 \( -\frac{2499309}{2048} a^{3} + \frac{8157429}{4096} a^{2} + \frac{8489043}{1024} a - \frac{22437243}{4096} \) \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{5}{2} a - 4\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{11}{2} a + 1\) , \( a^{3} - a^{2} - 9 a - 4\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+1\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+a^{2}+\frac{5}{2}a-4\right){x}^{2}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{11}{2}a+1\right){x}+a^{3}-a^{2}-9a-4$
4.2-b7 4.2-b 4.4.13968.1 \( 2^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.230369933$ $595.0569893$ 2.319782351 \( \frac{127972170891}{8} a^{3} - \frac{610814053521}{16} a^{2} - \frac{388881475065}{4} a + \frac{662195306133}{4} \) \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 3 a - 2\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a\) , \( -\frac{71}{2} a^{3} - 46 a^{2} + \frac{203}{2} a + 44\) , \( 516 a^{3} + 656 a^{2} - 1448 a - 628\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+3a-2\right){x}^{2}+\left(-\frac{71}{2}a^{3}-46a^{2}+\frac{203}{2}a+44\right){x}+516a^{3}+656a^{2}-1448a-628$
4.2-b8 4.2-b 4.4.13968.1 \( 2^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.076789977$ $595.0569893$ 2.319782351 \( \frac{2499309}{2048} a^{3} - \frac{6838425}{4096} a^{2} - \frac{4409397}{512} a + \frac{3669435}{1024} \) \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 3 a - 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 1\) , \( -a^{3} + \frac{3}{2} a^{2} + \frac{11}{2} a - 8\) , \( a^{3} - \frac{7}{2} a^{2} - \frac{13}{2} a + 13\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+3a-2\right){x}^{2}+\left(-a^{3}+\frac{3}{2}a^{2}+\frac{11}{2}a-8\right){x}+a^{3}-\frac{7}{2}a^{2}-\frac{13}{2}a+13$
4.2-b9 4.2-b 4.4.13968.1 \( 2^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.921479734$ $297.5284946$ 2.319782351 \( -\frac{13540475025}{4} a^{3} + 14479518933 a^{2} - \frac{18560142117}{2} a - \frac{23781491865}{4} \) \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a + 1\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 1\) , \( -\frac{187}{2} a^{3} + 223 a^{2} + \frac{1135}{2} a - 971\) , \( 49 a^{3} - 117 a^{2} - 298 a + 502\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a-1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-4a+1\right){x}^{2}+\left(-\frac{187}{2}a^{3}+223a^{2}+\frac{1135}{2}a-971\right){x}+49a^{3}-117a^{2}-298a+502$
4.2-b10 4.2-b 4.4.13968.1 \( 2^{2} \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $0.460739867$ $1190.113978$ 2.319782351 \( \frac{13540475025}{4} a^{3} + \frac{17296650657}{4} a^{2} - \frac{38094442155}{4} a - 4131043848 \) \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{7}{2} a + 3\) , \( 1\) , \( \frac{189}{2} a^{3} - \frac{119}{2} a^{2} - 741 a - 264\) , \( 143 a^{3} - \frac{177}{2} a^{2} - \frac{2243}{2} a - 407\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+1\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{7}{2}a+3\right){x}^{2}+\left(\frac{189}{2}a^{3}-\frac{119}{2}a^{2}-741a-264\right){x}+143a^{3}-\frac{177}{2}a^{2}-\frac{2243}{2}a-407$
4.2-b11 4.2-b 4.4.13968.1 \( 2^{2} \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $0.153579955$ $1190.113978$ 2.319782351 \( -\frac{26588277}{4} a^{3} + \frac{260982891}{64} a^{2} + \frac{834922323}{16} a + \frac{306974043}{16} \) \( \bigl[1\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{3}{2} a - 3\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( -a^{3} + a^{2} + 4 a - 4\) , \( \frac{3}{2} a^{3} + \frac{5}{2} a^{2} - 4 a - 4\bigr] \) ${y}^2+{x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+a^{2}+\frac{3}{2}a-3\right){x}^{2}+\left(-a^{3}+a^{2}+4a-4\right){x}+\frac{3}{2}a^{3}+\frac{5}{2}a^{2}-4a-4$
4.2-b12 4.2-b 4.4.13968.1 \( 2^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.307159911$ $595.0569893$ 2.319782351 \( -\frac{8685450106503327}{16} a^{3} + \frac{5328444787261821}{16} a^{2} + \frac{34093043623133667}{8} a + 1566064376677017 \) \( \bigl[1\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{3}{2} a - 3\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( -6 a^{3} - 19 a^{2} + 19 a + 26\) , \( \frac{135}{2} a^{3} + \frac{229}{2} a^{2} - 182 a - 148\bigr] \) ${y}^2+{x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+a^{2}+\frac{3}{2}a-3\right){x}^{2}+\left(-6a^{3}-19a^{2}+19a+26\right){x}+\frac{135}{2}a^{3}+\frac{229}{2}a^{2}-182a-148$
4.2-c1 4.2-c 4.4.13968.1 \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.452490233$ 3.589329868 \( \frac{8945482319277413784325011}{16} a^{3} - \frac{21348474961231757628600003}{16} a^{2} - \frac{6795874548186284776734387}{2} a + \frac{23144299352872525232815491}{4} \) \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( -12062 a^{3} + \frac{57713}{2} a^{2} + \frac{146797}{2} a - 125876\) , \( -1811281 a^{3} + 4323424 a^{2} + 11009111 a - 18756361\bigr] \) ${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a\right){x}^{2}+\left(-12062a^{3}+\frac{57713}{2}a^{2}+\frac{146797}{2}a-125876\right){x}-1811281a^{3}+4323424a^{2}+11009111a-18756361$
4.2-c2 4.2-c 4.4.13968.1 \( 2^{2} \) 0 $\Z/10\Z$ $\mathrm{SU}(2)$ $1$ $282.8063958$ 3.589329868 \( -\frac{3229550379}{512} a^{3} + \frac{13825034721}{512} a^{2} - \frac{2213871669}{128} a - \frac{1418628843}{128} \) \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a\) , \( a\) , \( -\frac{129}{2} a^{3} - 82 a^{2} + \frac{363}{2} a + 79\) , \( -1375 a^{3} - 1756 a^{2} + 3868 a + 1678\bigr] \) ${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){x}{y}+a{y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a\right){x}^{2}+\left(-\frac{129}{2}a^{3}-82a^{2}+\frac{363}{2}a+79\right){x}-1375a^{3}-1756a^{2}+3868a+1678$
4.2-c3 4.2-c 4.4.13968.1 \( 2^{2} \) 0 $\Z/10\Z$ $\mathrm{SU}(2)$ $1$ $282.8063958$ 3.589329868 \( \frac{473992695}{65536} a^{3} - \frac{1067733171}{65536} a^{2} - \frac{779105385}{16384} a + \frac{1277601849}{16384} \) \( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 2 a - 2\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( -\frac{11}{2} a^{3} - \frac{9}{2} a^{2} + 22 a + 11\) , \( -34 a^{3} + \frac{39}{2} a^{2} + \frac{525}{2} a + 96\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+2a-2\right){x}^{2}+\left(-\frac{11}{2}a^{3}-\frac{9}{2}a^{2}+22a+11\right){x}-34a^{3}+\frac{39}{2}a^{2}+\frac{525}{2}a+96$
4.2-c4 4.2-c 4.4.13968.1 \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.452490233$ 3.589329868 \( \frac{90654800674642778406799989}{8} a^{3} + \frac{115804904338226014889775039}{8} a^{2} - \frac{127520733137203414315612503}{4} a - \frac{27660355613887103422048503}{2} \) \( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( -2635 a^{3} + \frac{11957}{2} a^{2} + \frac{35001}{2} a - 28751\) , \( -195845 a^{3} + 457861 a^{2} + 1234695 a - 2070128\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-1\right){x}^{2}+\left(-2635a^{3}+\frac{11957}{2}a^{2}+\frac{35001}{2}a-28751\right){x}-195845a^{3}+457861a^{2}+1234695a-2070128$
4.2-c5 4.2-c 4.4.13968.1 \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.452490233$ 3.589329868 \( -\frac{90654800674642778406799989}{8} a^{3} + \frac{193884653181077175055087503}{4} a^{2} - \frac{248532744425973536368725039}{8} a - \frac{79611591858543224511421995}{4} \) \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 3 a - 2\) , \( 0\) , \( 2637 a^{3} - 1936 a^{2} - 21544 a - 7902\) , \( 199062 a^{3} - 131508 a^{2} - 1587741 a - 582554\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+1\right){x}{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+3a-2\right){x}^{2}+\left(2637a^{3}-1936a^{2}-21544a-7902\right){x}+199062a^{3}-131508a^{2}-1587741a-582554$
4.2-c6 4.2-c 4.4.13968.1 \( 2^{2} \) 0 $\Z/10\Z$ $\mathrm{SU}(2)$ $1$ $282.8063958$ 3.589329868 \( -\frac{473992695}{65536} a^{3} + \frac{177122457}{32768} a^{2} + \frac{3829909797}{65536} a + \frac{350061345}{16384} \) \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a + 1\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( 5 a^{3} - \frac{39}{2} a^{2} + \frac{3}{2} a + 23\) , \( \frac{67}{2} a^{3} - \frac{163}{2} a^{2} - 199 a + 343\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+1\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-4a+1\right){x}^{2}+\left(5a^{3}-\frac{39}{2}a^{2}+\frac{3}{2}a+23\right){x}+\frac{67}{2}a^{3}-\frac{163}{2}a^{2}-199a+343$
4.2-c7 4.2-c 4.4.13968.1 \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.452490233$ 3.589329868 \( -\frac{8945482319277413784325011}{16} a^{3} + \frac{2743985998300241862187515}{8} a^{2} + \frac{70227499350121552118100069}{16} a + \frac{6451802096011369718277969}{4} \) \( \bigl[1\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{3}{2} a - 3\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( -4418 a^{3} - 5789 a^{2} + 12142 a + 5302\) , \( -\frac{1419163}{2} a^{3} - \frac{1815803}{2} a^{2} + 1993125 a + 865020\bigr] \) ${y}^2+{x}{y}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+a^{2}+\frac{3}{2}a-3\right){x}^{2}+\left(-4418a^{3}-5789a^{2}+12142a+5302\right){x}-\frac{1419163}{2}a^{3}-\frac{1815803}{2}a^{2}+1993125a+865020$
4.2-c8 4.2-c 4.4.13968.1 \( 2^{2} \) 0 $\Z/10\Z$ $\mathrm{SU}(2)$ $1$ $282.8063958$ 3.589329868 \( \frac{3229550379}{512} a^{3} + \frac{129261987}{16} a^{2} - \frac{9105931629}{512} a - \frac{1967258853}{256} \) \( \bigl[1\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{3}{2} a - 3\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 2\) , \( -\frac{31}{2} a^{3} + \frac{75}{2} a^{2} + 95 a - 165\) , \( \frac{209}{2} a^{3} - \frac{495}{2} a^{2} - 634 a + 1039\bigr] \) ${y}^2+{x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+a^{2}+\frac{3}{2}a-3\right){x}^{2}+\left(-\frac{31}{2}a^{3}+\frac{75}{2}a^{2}+95a-165\right){x}+\frac{209}{2}a^{3}-\frac{495}{2}a^{2}-634a+1039$
4.2-d1 4.2-d 4.4.13968.1 \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $198.4847243$ 0.839711265 \( -\frac{8945482319277413784325011}{16} a^{3} + \frac{2743985998300241862187515}{8} a^{2} + \frac{70227499350121552118100069}{16} a + \frac{6451802096011369718277969}{4} \) \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 2\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( -4418 a^{3} - 5789 a^{2} + 12142 a + 5301\) , \( 709581 a^{3} + \frac{1815801}{2} a^{2} - \frac{3986249}{2} a - 865020\bigr] \) ${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+2\right){x}^{2}+\left(-4418a^{3}-5789a^{2}+12142a+5301\right){x}+709581a^{3}+\frac{1815801}{2}a^{2}-\frac{3986249}{2}a-865020$
4.2-d2 4.2-d 4.4.13968.1 \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $198.4847243$ 0.839711265 \( \frac{3229550379}{512} a^{3} + \frac{129261987}{16} a^{2} - \frac{9105931629}{512} a - \frac{1967258853}{256} \) \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 2\) , \( a\) , \( -\frac{31}{2} a^{3} + \frac{75}{2} a^{2} + 95 a - 164\) , \( -105 a^{3} + 247 a^{2} + 636 a - 1040\bigr] \) ${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){x}{y}+a{y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+2\right){x}^{2}+\left(-\frac{31}{2}a^{3}+\frac{75}{2}a^{2}+95a-164\right){x}-105a^{3}+247a^{2}+636a-1040$
4.2-d3 4.2-d 4.4.13968.1 \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $198.4847243$ 0.839711265 \( -\frac{473992695}{65536} a^{3} + \frac{177122457}{32768} a^{2} + \frac{3829909797}{65536} a + \frac{350061345}{16384} \) \( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( \frac{7}{2} a^{3} - \frac{37}{2} a^{2} + 11 a + 21\) , \( -\frac{59}{2} a^{3} + 63 a^{2} + \frac{413}{2} a - 324\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a\right){x}^{2}+\left(\frac{7}{2}a^{3}-\frac{37}{2}a^{2}+11a+21\right){x}-\frac{59}{2}a^{3}+63a^{2}+\frac{413}{2}a-324$
4.2-d4 4.2-d 4.4.13968.1 \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $198.4847243$ 0.839711265 \( -\frac{90654800674642778406799989}{8} a^{3} + \frac{193884653181077175055087503}{4} a^{2} - \frac{248532744425973536368725039}{8} a - \frac{79611591858543224511421995}{4} \) \( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 3\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a\) , \( \frac{5277}{2} a^{3} - 1935 a^{2} - \frac{43103}{2} a - 7902\) , \( -193084 a^{3} + 126489 a^{2} + 1537187 a + 564100\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+3\right){x}^{2}+\left(\frac{5277}{2}a^{3}-1935a^{2}-\frac{43103}{2}a-7902\right){x}-193084a^{3}+126489a^{2}+1537187a+564100$
4.2-d5 4.2-d 4.4.13968.1 \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $198.4847243$ 0.839711265 \( \frac{90654800674642778406799989}{8} a^{3} + \frac{115804904338226014889775039}{8} a^{2} - \frac{127520733137203414315612503}{4} a - \frac{27660355613887103422048503}{2} \) \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{5}{2} a - 4\) , \( 0\) , \( -2637 a^{3} + 5975 a^{2} + 17505 a - 28745\) , \( 199062 a^{3} - 465678 a^{2} - 1253571 a + 2102741\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+1\right){x}{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+a^{2}+\frac{5}{2}a-4\right){x}^{2}+\left(-2637a^{3}+5975a^{2}+17505a-28745\right){x}+199062a^{3}-465678a^{2}-1253571a+2102741$
4.2-d6 4.2-d 4.4.13968.1 \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $198.4847243$ 0.839711265 \( \frac{473992695}{65536} a^{3} - \frac{1067733171}{65536} a^{2} - \frac{779105385}{16384} a + \frac{1277601849}{16384} \) \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{7}{2} a + 3\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -4 a^{3} - \frac{13}{2} a^{2} + \frac{27}{2} a + 17\) , \( 29 a^{3} - \frac{49}{2} a^{2} - \frac{487}{2} a - 85\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+1\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{7}{2}a+3\right){x}^{2}+\left(-4a^{3}-\frac{13}{2}a^{2}+\frac{27}{2}a+17\right){x}+29a^{3}-\frac{49}{2}a^{2}-\frac{487}{2}a-85$
4.2-d7 4.2-d 4.4.13968.1 \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $198.4847243$ 0.839711265 \( \frac{8945482319277413784325011}{16} a^{3} - \frac{21348474961231757628600003}{16} a^{2} - \frac{6795874548186284776734387}{2} a + \frac{23144299352872525232815491}{4} \) \( \bigl[1\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 2 a - 1\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( -12062 a^{3} + \frac{57713}{2} a^{2} + \frac{146797}{2} a - 125875\) , \( \frac{3622561}{2} a^{3} - 4323425 a^{2} - \frac{22018221}{2} a + 18756361\bigr] \) ${y}^2+{x}{y}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+2a-1\right){x}^{2}+\left(-12062a^{3}+\frac{57713}{2}a^{2}+\frac{146797}{2}a-125875\right){x}+\frac{3622561}{2}a^{3}-4323425a^{2}-\frac{22018221}{2}a+18756361$
4.2-d8 4.2-d 4.4.13968.1 \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $198.4847243$ 0.839711265 \( -\frac{3229550379}{512} a^{3} + \frac{13825034721}{512} a^{2} - \frac{2213871669}{128} a - \frac{1418628843}{128} \) \( \bigl[1\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 2 a - 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 2\) , \( -\frac{129}{2} a^{3} - 82 a^{2} + \frac{363}{2} a + 78\) , \( \frac{2749}{2} a^{3} + \frac{3511}{2} a^{2} - 3866 a - 1679\bigr] \) ${y}^2+{x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+2a-1\right){x}^{2}+\left(-\frac{129}{2}a^{3}-82a^{2}+\frac{363}{2}a+78\right){x}+\frac{2749}{2}a^{3}+\frac{3511}{2}a^{2}-3866a-1679$
4.2-e1 4.2-e 4.4.13968.1 \( 2^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.307159911$ $297.5284946$ 2.319782351 \( -\frac{26588277}{4} a^{3} + \frac{260982891}{64} a^{2} + \frac{834922323}{16} a + \frac{306974043}{16} \) \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 2\) , \( 1\) , \( -a^{3} + a^{2} + 4 a - 4\) , \( -\frac{3}{2} a^{3} - \frac{5}{2} a^{2} + 4 a + 3\bigr] \) ${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+2\right){x}^{2}+\left(-a^{3}+a^{2}+4a-4\right){x}-\frac{3}{2}a^{3}-\frac{5}{2}a^{2}+4a+3$
4.2-e2 4.2-e 4.4.13968.1 \( 2^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.614319822$ $18.59553091$ 2.319782351 \( -\frac{8685450106503327}{16} a^{3} + \frac{5328444787261821}{16} a^{2} + \frac{34093043623133667}{8} a + 1566064376677017 \) \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 2\) , \( 1\) , \( -6 a^{3} - 19 a^{2} + 19 a + 26\) , \( -\frac{135}{2} a^{3} - \frac{229}{2} a^{2} + 182 a + 147\bigr] \) ${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-2\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+2\right){x}^{2}+\left(-6a^{3}-19a^{2}+19a+26\right){x}-\frac{135}{2}a^{3}-\frac{229}{2}a^{2}+182a+147$
4.2-e3 4.2-e 4.4.13968.1 \( 2^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.921479734$ $297.5284946$ 2.319782351 \( \frac{13540475025}{4} a^{3} + \frac{17296650657}{4} a^{2} - \frac{38094442155}{4} a - 4131043848 \) \( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 2 a - 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 2\) , \( \frac{187}{2} a^{3} - 58 a^{2} - \frac{1473}{2} a - 271\) , \( -49 a^{3} + 30 a^{2} + 383 a + 138\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+2\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+2a-2\right){x}^{2}+\left(\frac{187}{2}a^{3}-58a^{2}-\frac{1473}{2}a-271\right){x}-49a^{3}+30a^{2}+383a+138$
4.2-e4 4.2-e 4.4.13968.1 \( 2^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.076789977$ $595.0569893$ 2.319782351 \( -\frac{2499309}{2048} a^{3} + \frac{8157429}{4096} a^{2} + \frac{8489043}{1024} a - \frac{22437243}{4096} \) \( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 2\) , \( 3 a^{3} + \frac{7}{2} a^{2} - \frac{25}{2} a - 10\) , \( \frac{9}{2} a^{3} + \frac{15}{2} a^{2} - 9 a - 5\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-1\right){x}^{2}+\left(3a^{3}+\frac{7}{2}a^{2}-\frac{25}{2}a-10\right){x}+\frac{9}{2}a^{3}+\frac{15}{2}a^{2}-9a-5$
4.2-e5 4.2-e 4.4.13968.1 \( 2^{2} \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $0.460739867$ $1190.113978$ 2.319782351 \( -\frac{13540475025}{4} a^{3} + 14479518933 a^{2} - \frac{18560142117}{2} a - \frac{23781491865}{4} \) \( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a\) , \( 1\) , \( -95 a^{3} + \frac{449}{2} a^{2} + \frac{1159}{2} a - 971\) , \( -143 a^{3} + \frac{681}{2} a^{2} + \frac{1739}{2} a - 1474\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a\right){x}^{2}+\left(-95a^{3}+\frac{449}{2}a^{2}+\frac{1159}{2}a-971\right){x}-143a^{3}+\frac{681}{2}a^{2}+\frac{1739}{2}a-1474$
4.2-e6 4.2-e 4.4.13968.1 \( 2^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.842959468$ $74.38212366$ 2.319782351 \( \frac{127972170891}{8} a^{3} - \frac{610814053521}{16} a^{2} - \frac{388881475065}{4} a + \frac{662195306133}{4} \) \( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 3\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 1\) , \( -33 a^{3} - \frac{89}{2} a^{2} + \frac{181}{2} a + 44\) , \( -664 a^{3} - 845 a^{2} + 1862 a + 809\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a-1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+3\right){x}^{2}+\left(-33a^{3}-\frac{89}{2}a^{2}+\frac{181}{2}a+44\right){x}-664a^{3}-845a^{2}+1862a+809$
4.2-e7 4.2-e 4.4.13968.1 \( 2^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.614319822$ $74.38212366$ 2.319782351 \( \frac{2499309}{2048} a^{3} - \frac{6838425}{4096} a^{2} - \frac{4409397}{512} a + \frac{3669435}{1024} \) \( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 3\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 2\) , \( a^{3} + \frac{7}{2} a^{2} - \frac{5}{2} a - 8\) , \( \frac{3}{2} a^{3} + \frac{15}{2} a^{2} - 23\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{3}{2}a+3\right){x}^{2}+\left(a^{3}+\frac{7}{2}a^{2}-\frac{5}{2}a-8\right){x}+\frac{3}{2}a^{3}+\frac{15}{2}a^{2}-23$
4.2-e8 4.2-e 4.4.13968.1 \( 2^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.230369933$ $595.0569893$ 2.319782351 \( -\frac{127972170891}{8} a^{3} + \frac{157018971825}{16} a^{2} + \frac{502330245489}{4} a + \frac{738385612533}{16} \) \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{7}{2} a + 3\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 1\) , \( 8 a^{3} - \frac{15}{2} a^{2} - \frac{121}{2} a - 11\) , \( -\frac{47}{2} a^{3} + \frac{27}{2} a^{2} + 183 a + 76\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a-1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{7}{2}a+3\right){x}^{2}+\left(8a^{3}-\frac{15}{2}a^{2}-\frac{121}{2}a-11\right){x}-\frac{47}{2}a^{3}+\frac{27}{2}a^{2}+183a+76$
4.2-e9 4.2-e 4.4.13968.1 \( 2^{2} \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $0.153579955$ $1190.113978$ 2.319782351 \( \frac{26588277}{4} a^{3} - \frac{1015254405}{64} a^{2} - \frac{1292708889}{32} a + \frac{4403155923}{64} \) \( \bigl[1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 2\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 1\) , \( 2 a^{3} - 3 a^{2} - 7 a + 1\) , \( \frac{9}{2} a^{2} - \frac{21}{2} a - 4\bigr] \) ${y}^2+{x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+2\right){x}^{2}+\left(2a^{3}-3a^{2}-7a+1\right){x}+\frac{9}{2}a^{2}-\frac{21}{2}a-4$
4.2-e10 4.2-e 4.4.13968.1 \( 2^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.307159911$ $595.0569893$ 2.319782351 \( \frac{8685450106503327}{16} a^{3} - 1295494095765510 a^{2} - \frac{52786626501280995}{16} a + \frac{22471527988464525}{4} \) \( \bigl[1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 2\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 1\) , \( 7 a^{3} - 38 a^{2} + 33 a + 21\) , \( -61 a^{3} + \frac{559}{2} a^{2} - \frac{429}{2} a - 128\bigr] \) ${y}^2+{x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-2a+2\right){x}^{2}+\left(7a^{3}-38a^{2}+33a+21\right){x}-61a^{3}+\frac{559}{2}a^{2}-\frac{429}{2}a-128$
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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.