| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 2.1-a1 |
2.1-a |
$2$ |
$3$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2^{18} \) |
$4.14528$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$1.728190687$ |
$5.230065894$ |
1.312218445 |
\( \frac{5794347734441}{512} a^{2} - \frac{4650229820901}{128} a - \frac{5243330195397}{512} \) |
\( \bigl[a + 1\) , \( 0\) , \( a^{2} - a - 5\) , \( -383 a^{2} - 946 a - 219\) , \( -53417 a^{2} - 131990 a - 30786\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(-383a^{2}-946a-219\right){x}-53417a^{2}-131990a-30786$ |
| 2.1-a2 |
2.1-a |
$2$ |
$3$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2^{6} \) |
$4.14528$ |
$(a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$0.576063562$ |
$141.2117791$ |
1.312218445 |
\( \frac{2517}{8} a^{2} - 1396 a + \frac{9331}{8} \) |
\( \bigl[a + 1\) , \( 0\) , \( a^{2} - a - 5\) , \( 42 a^{2} + 104 a + 26\) , \( 1916 a^{2} + 4732 a + 1098\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(42a^{2}+104a+26\right){x}+1916a^{2}+4732a+1098$ |
| 2.2-a1 |
2.2-a |
$2$ |
$3$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
2.2 |
\( 2 \) |
\( - 2^{18} \) |
$4.14528$ |
$(-a^2+2a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$3.174628814$ |
$2.907502140$ |
1.340047874 |
\( -\frac{434581617174085}{262144} a^{2} - \frac{536914377368745}{131072} a - \frac{125232737745231}{131072} \) |
\( \bigl[a^{2} - 2 a - 4\) , \( a^{2} - 3 a - 6\) , \( 1\) , \( -1154 a^{2} - 2876 a - 668\) , \( -68297 a^{2} - 168794 a - 39365\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){x}{y}+{y}={x}^{3}+\left(a^{2}-3a-6\right){x}^{2}+\left(-1154a^{2}-2876a-668\right){x}-68297a^{2}-168794a-39365$ |
| 2.2-a2 |
2.2-a |
$2$ |
$3$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
2.2 |
\( 2 \) |
\( - 2^{6} \) |
$4.14528$ |
$(-a^2+2a+5)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1.058209604$ |
$78.50255779$ |
1.340047874 |
\( -\frac{14277}{64} a^{2} - \frac{5161}{32} a + \frac{21041}{32} \) |
\( \bigl[a^{2} - 2 a - 4\) , \( a^{2} - 3 a - 6\) , \( 1\) , \( -9 a^{2} - 46 a - 8\) , \( -86 a^{2} - 250 a - 60\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){x}{y}+{y}={x}^{3}+\left(a^{2}-3a-6\right){x}^{2}+\left(-9a^{2}-46a-8\right){x}-86a^{2}-250a-60$ |
| 4.2-a1 |
4.2-a |
$2$ |
$2$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{21} \) |
$4.65292$ |
$(a), (-a^2+2a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$27.13428349$ |
2.297960024 |
\( -\frac{59189}{128} a^{2} + \frac{68991}{128} a + \frac{439297}{128} \) |
\( \bigl[a^{2} - a - 5\) , \( -a^{2} + 3 a + 5\) , \( a^{2} - 2 a - 5\) , \( 1958156 a^{2} - 2468668 a - 15021629\) , \( 1956342685 a^{2} - 2466383495 a - 15007727221\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-2a-5\right){y}={x}^{3}+\left(-a^{2}+3a+5\right){x}^{2}+\left(1958156a^{2}-2468668a-15021629\right){x}+1956342685a^{2}-2466383495a-15007727221$ |
| 4.2-a2 |
4.2-a |
$2$ |
$2$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{21} \) |
$4.65292$ |
$(a), (-a^2+2a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$27.13428349$ |
2.297960024 |
\( \frac{697091605}{16384} a^{2} + \frac{275832505}{8192} a + \frac{55243967}{8192} \) |
\( \bigl[1\) , \( a^{2} - 3 a - 5\) , \( a^{2} - 2 a - 5\) , \( -7 a^{2} + 7 a + 62\) , \( 31 a^{2} - 40 a - 235\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-2a-5\right){y}={x}^{3}+\left(a^{2}-3a-5\right){x}^{2}+\left(-7a^{2}+7a+62\right){x}+31a^{2}-40a-235$ |
| 5.1-a1 |
5.1-a |
$2$ |
$2$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( 5 \) |
$4.82923$ |
$(a^2+3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$269.6279788$ |
1.631026554 |
\( \frac{26754561}{5} a^{2} + 13209506 a + \frac{15409862}{5} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -21 a^{2} + 70 a + 9\) , \( -152 a^{2} + 488 a + 137\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-21a^{2}+70a+9\right){x}-152a^{2}+488a+137$ |
| 5.1-a2 |
5.1-a |
$2$ |
$2$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{2} \) |
$4.82923$ |
$(a^2+3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$134.8139894$ |
1.631026554 |
\( \frac{1357224623}{25} a^{2} - \frac{871596098}{5} a - \frac{1224795174}{25} \) |
\( \bigl[a\) , \( -a^{2} + a + 6\) , \( 1\) , \( 3164 a^{2} - 3960 a - 24374\) , \( -179147 a^{2} + 226000 a + 1373782\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(3164a^{2}-3960a-24374\right){x}-179147a^{2}+226000a+1373782$ |
| 5.1-b1 |
5.1-b |
$1$ |
$1$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( 5^{2} \) |
$4.82923$ |
$(a^2+3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.032520840$ |
$283.2134162$ |
1.337158542 |
\( -\frac{30704}{25} a^{2} - \frac{23041}{5} a - \frac{25273}{25} \) |
\( \bigl[a^{2} - 2 a - 5\) , \( a^{2} - 2 a - 4\) , \( a^{2} - 2 a - 4\) , \( a^{2} - 12 a - 10\) , \( 7 a^{2} + a - 3\bigr] \) |
${y}^2+\left(a^{2}-2a-5\right){x}{y}+\left(a^{2}-2a-4\right){y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(a^{2}-12a-10\right){x}+7a^{2}+a-3$ |
| 8.1-a1 |
8.1-a |
$1$ |
$1$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{6} \) |
$5.22273$ |
$(a), (-a^2+2a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$38.24841785$ |
1.850970672 |
\( \frac{62402075}{4} a^{2} - \frac{38885577}{2} a - \frac{240913455}{2} \) |
\( \bigl[a^{2} - 2 a - 4\) , \( a^{2} - 3 a - 5\) , \( a^{2} - a - 4\) , \( 884 a^{2} + 2155 a + 496\) , \( -61119 a^{2} - 151063 a - 35233\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{2}-3a-5\right){x}^{2}+\left(884a^{2}+2155a+496\right){x}-61119a^{2}-151063a-35233$ |
| 8.2-a1 |
8.2-a |
$1$ |
$1$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{10} \) |
$5.22273$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.375606330$ |
$97.71608461$ |
5.328516040 |
\( -22814 a^{2} - 82680 a - 69290 \) |
\( \bigl[a^{2} - a - 4\) , \( -a^{2} + a + 6\) , \( a^{2} - 2 a - 4\) , \( -57 a^{2} - 126 a - 8\) , \( 641 a^{2} + 1600 a + 398\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-2a-4\right){y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(-57a^{2}-126a-8\right){x}+641a^{2}+1600a+398$ |
| 8.4-a1 |
8.4-a |
$1$ |
$1$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
8.4 |
\( 2^{3} \) |
\( - 2^{10} \) |
$5.22273$ |
$(-a^2+2a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$111.5787253$ |
5.399672979 |
\( 140 a^{2} - 264 a - 184 \) |
\( \bigl[0\) , \( a^{2} - 2 a - 4\) , \( a + 1\) , \( 4026 a^{2} + 9945 a + 2323\) , \( -630194 a^{2} - 1557147 a - 363133\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(4026a^{2}+9945a+2323\right){x}-630194a^{2}-1557147a-363133$ |
| 10.1-a1 |
10.1-a |
$2$ |
$3$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{4} \cdot 5^{2} \) |
$5.42062$ |
$(a), (a^2+3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 2^{3} \) |
$1.004802875$ |
$0.790103181$ |
4.149296767 |
\( \frac{3783438172851421}{25} a^{2} - \frac{25876736365578469}{20} a - \frac{34760446700441217}{100} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a^{2} - a - 5\) , \( -1589 a^{2} - 3523 a - 808\) , \( -109335 a^{2} - 266176 a - 61969\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-1589a^{2}-3523a-808\right){x}-109335a^{2}-266176a-61969$ |
| 10.1-a2 |
10.1-a |
$2$ |
$3$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{12} \cdot 5^{6} \) |
$5.42062$ |
$(a), (a^2+3a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$0.334934291$ |
$21.33278588$ |
4.149296767 |
\( \frac{25105502029}{250000} a^{2} - \frac{35622023071}{200000} a - \frac{735319375883}{1000000} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a^{2} - a - 5\) , \( -19 a^{2} - 43 a - 8\) , \( -190 a^{2} - 470 a - 115\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-19a^{2}-43a-8\right){x}-190a^{2}-470a-115$ |
| 10.1-b1 |
10.1-b |
$1$ |
$1$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{6} \cdot 5^{4} \) |
$5.42062$ |
$(a), (a^2+3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \cdot 3 \) |
$0.005944933$ |
$225.7554243$ |
2.338157484 |
\( \frac{48318947}{5000} a^{2} - \frac{7605983}{250} a - \frac{54718311}{5000} \) |
\( \bigl[a^{2} - 2 a - 5\) , \( -a - 1\) , \( a^{2} - a - 5\) , \( 65 a^{2} - 82 a - 492\) , \( -603 a^{2} + 758 a + 4627\bigr] \) |
${y}^2+\left(a^{2}-2a-5\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(65a^{2}-82a-492\right){x}-603a^{2}+758a+4627$ |
| 10.2-a1 |
10.2-a |
$2$ |
$2$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{7} \cdot 5^{14} \) |
$5.42062$ |
$(-a^2+2a+5), (a^2+3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \cdot 7 \) |
$1$ |
$21.07219795$ |
7.138285930 |
\( \frac{7280816541121809}{781250000000} a^{2} - \frac{2419204110032927}{78125000000} a - \frac{2726084397087821}{390625000000} \) |
\( \bigl[a\) , \( a^{2} - 3 a - 5\) , \( 1\) , \( -128 a^{2} - 287 a + 12\) , \( 3111 a^{2} + 7627 a + 1677\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a^{2}-3a-5\right){x}^{2}+\left(-128a^{2}-287a+12\right){x}+3111a^{2}+7627a+1677$ |
| 10.2-a2 |
10.2-a |
$2$ |
$2$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{14} \cdot 5^{7} \) |
$5.42062$ |
$(-a^2+2a+5), (a^2+3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$84.28879183$ |
7.138285930 |
\( \frac{494962130018329}{1280000000} a^{2} + \frac{122288483377513}{128000000} a + \frac{143694647812299}{640000000} \) |
\( \bigl[a\) , \( -a + 1\) , \( a^{2} - 2 a - 5\) , \( -18858 a^{2} - 46602 a - 10868\) , \( 4585883 a^{2} + 11331236 a + 2642473\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-2a-5\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-18858a^{2}-46602a-10868\right){x}+4585883a^{2}+11331236a+2642473$ |
| 10.2-b1 |
10.2-b |
$1$ |
$1$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2 \cdot 5 \) |
$5.42062$ |
$(-a^2+2a+5), (a^2+3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$90.92615988$ |
2.200112642 |
\( \frac{38399}{10} a^{2} - 4966 a - \frac{145116}{5} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 17 a^{2} - 31 a - 93\) , \( 60 a^{2} - 116 a - 326\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(17a^{2}-31a-93\right){x}+60a^{2}-116a-326$ |
| 10.2-c1 |
10.2-c |
$2$ |
$2$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{3} \cdot 5^{2} \) |
$5.42062$ |
$(-a^2+2a+5), (a^2+3a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.503180940$ |
$73.03653761$ |
3.984728748 |
\( \frac{15338890368409}{200} a^{2} - \frac{4924066224407}{20} a - \frac{6940096464821}{100} \) |
\( \bigl[a\) , \( a^{2} - 2 a - 5\) , \( 1\) , \( 6928 a^{2} + 17116 a + 3998\) , \( 4628678 a^{2} + 11436975 a + 2667133\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(6928a^{2}+17116a+3998\right){x}+4628678a^{2}+11436975a+2667133$ |
| 10.2-c2 |
10.2-c |
$2$ |
$2$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{6} \cdot 5 \) |
$5.42062$ |
$(-a^2+2a+5), (a^2+3a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.751590470$ |
$146.0730752$ |
3.984728748 |
\( -\frac{712113919}{320} a^{2} + \frac{84657873}{32} a + \frac{2822434691}{160} \) |
\( \bigl[a\) , \( -a^{2} + a + 5\) , \( a^{2} - 2 a - 5\) , \( -174211083904711869 a^{2} - 430457386108350738 a - 100383940160130786\) , \( 120367116963804400563678682 a^{2} + 297414569614740721170535174 a + 69357960444990948034971731\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-2a-5\right){y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(-174211083904711869a^{2}-430457386108350738a-100383940160130786\right){x}+120367116963804400563678682a^{2}+297414569614740721170535174a+69357960444990948034971731$ |
| 10.2-d1 |
10.2-d |
$4$ |
$4$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{8} \cdot 5^{3} \) |
$5.42062$ |
$(-a^2+2a+5), (a^2+3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$23.84364270$ |
0.865406058 |
\( \frac{241328052482829}{32000} a^{2} + \frac{59629637280413}{3200} a + \frac{69529037877799}{16000} \) |
\( \bigl[a^{2} - a - 5\) , \( a^{2} - 3 a - 6\) , \( 1\) , \( 2378382467 a^{2} - 2998453860 a - 18245328666\) , \( -347753573127699 a^{2} + 438416889306032 a + 2667728309986095\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+{y}={x}^{3}+\left(a^{2}-3a-6\right){x}^{2}+\left(2378382467a^{2}-2998453860a-18245328666\right){x}-347753573127699a^{2}+438416889306032a+2667728309986095$ |
| 10.2-d2 |
10.2-d |
$4$ |
$4$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{32} \cdot 5^{3} \) |
$5.42062$ |
$(-a^2+2a+5), (a^2+3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$23.84364270$ |
0.865406058 |
\( \frac{36803041646522561}{536870912000} a^{2} - \frac{11815232523222383}{53687091200} a - \frac{16169642844731709}{268435456000} \) |
\( \bigl[a^{2} - a - 5\) , \( a^{2} - 2 a - 5\) , \( a^{2} - 2 a - 4\) , \( -159 a^{2} + 513 a + 136\) , \( -2893 a^{2} + 9288 a + 2615\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-2a-4\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(-159a^{2}+513a+136\right){x}-2893a^{2}+9288a+2615$ |
| 10.2-d3 |
10.2-d |
$4$ |
$4$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{8} \cdot 5^{12} \) |
$5.42062$ |
$(-a^2+2a+5), (a^2+3a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$23.84364270$ |
0.865406058 |
\( -\frac{2779620630758502488353}{62500000000} a^{2} + \frac{350429809288752812559}{6250000000} a + \frac{10661679375753987507357}{31250000000} \) |
\( \bigl[1\) , \( a^{2} - a - 5\) , \( 0\) , \( 1184774 a^{2} - 1493651 a - 9088798\) , \( -1340528600 a^{2} + 1690019660 a + 10283621465\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(1184774a^{2}-1493651a-9088798\right){x}-1340528600a^{2}+1690019660a+10283621465$ |
| 10.2-d4 |
10.2-d |
$4$ |
$4$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{16} \cdot 5^{6} \) |
$5.42062$ |
$(-a^2+2a+5), (a^2+3a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$47.68728541$ |
0.865406058 |
\( -\frac{60647740196907}{1024000000} a^{2} + \frac{14832731893221}{102400000} a + \frac{313002971395583}{512000000} \) |
\( \bigl[1\) , \( a^{2} - a - 5\) , \( 0\) , \( 74079 a^{2} - 93391 a - 568283\) , \( -21009117 a^{2} + 26486434 a + 161167620\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(74079a^{2}-93391a-568283\right){x}-21009117a^{2}+26486434a+161167620$ |
| 10.2-e1 |
10.2-e |
$4$ |
$6$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{9} \cdot 5^{18} \) |
$5.42062$ |
$(-a^2+2a+5), (a^2+3a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$12.72246725$ |
$4.677332236$ |
2.159816661 |
\( -\frac{271951069979894215569}{1953125000000000} a^{2} + \frac{34683514231556514207}{195312500000000} a + \frac{1037966303949989677261}{976562500000000} \) |
\( \bigl[a\) , \( a - 1\) , \( a^{2} - a - 5\) , \( 181363 a^{2} - 228548 a - 1391631\) , \( 80070747 a^{2} - 100945196 a - 614251321\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(181363a^{2}-228548a-1391631\right){x}+80070747a^{2}-100945196a-614251321$ |
| 10.2-e2 |
10.2-e |
$4$ |
$6$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{3} \cdot 5^{6} \) |
$5.42062$ |
$(-a^2+2a+5), (a^2+3a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$4.240822418$ |
$126.2879703$ |
2.159816661 |
\( \frac{2730695943879}{125000} a^{2} + \frac{674754175863}{12500} a + \frac{787155099349}{62500} \) |
\( \bigl[a\) , \( a - 1\) , \( a^{2} - a - 5\) , \( 8103 a^{2} - 10223 a - 62131\) , \( -642778 a^{2} + 810362 a + 4930942\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(8103a^{2}-10223a-62131\right){x}-642778a^{2}+810362a+4930942$ |
| 10.2-e3 |
10.2-e |
$4$ |
$6$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{6} \cdot 5^{3} \) |
$5.42062$ |
$(-a^2+2a+5), (a^2+3a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$2.120411209$ |
$252.5759407$ |
2.159816661 |
\( -\frac{30466345351}{8000} a^{2} + \frac{3843818953}{800} a + \frac{116897418219}{4000} \) |
\( \bigl[a\) , \( -a^{2} + 3 a + 4\) , \( a^{2} - a - 5\) , \( 14 a^{2} + 25 a - 252\) , \( -127 a^{2} + 50 a + 1359\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(-a^{2}+3a+4\right){x}^{2}+\left(14a^{2}+25a-252\right){x}-127a^{2}+50a+1359$ |
| 10.2-e4 |
10.2-e |
$4$ |
$6$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{18} \cdot 5^{9} \) |
$5.42062$ |
$(-a^2+2a+5), (a^2+3a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$6.361233627$ |
$9.354664473$ |
2.159816661 |
\( \frac{5101970085872120721}{512000000000} a^{2} - \frac{1635880022575669663}{51200000000} a - \frac{2305351073307756749}{256000000000} \) |
\( \bigl[a\) , \( -a^{2} + 3 a + 4\) , \( a^{2} - a - 5\) , \( -1166 a^{2} + 3870 a + 618\) , \( -52561 a^{2} + 169235 a + 45814\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(-a^{2}+3a+4\right){x}^{2}+\left(-1166a^{2}+3870a+618\right){x}-52561a^{2}+169235a+45814$ |
| 10.2-f1 |
10.2-f |
$1$ |
$1$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{9} \cdot 5 \) |
$5.42062$ |
$(-a^2+2a+5), (a^2+3a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3^{2} \) |
$1$ |
$7.413264702$ |
1.614388606 |
\( -\frac{115133512368921}{2560} a^{2} + \frac{36959975388311}{256} a + \frac{52092153275189}{1280} \) |
\( \bigl[a^{2} - a - 5\) , \( a^{2} - 3 a - 4\) , \( a^{2} - a - 4\) , \( -4 a^{2} - 19 a - 13\) , \( 20 a^{2} + 62 a + 10\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{2}-3a-4\right){x}^{2}+\left(-4a^{2}-19a-13\right){x}+20a^{2}+62a+10$ |
| 10.2-g1 |
10.2-g |
$2$ |
$2$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{18} \cdot 5^{5} \) |
$5.42062$ |
$(-a^2+2a+5), (a^2+3a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.593089482$ |
$73.14859021$ |
1.574611826 |
\( -\frac{90109075315911}{819200000} a^{2} + \frac{8639138500233}{81920000} a + \frac{407842317154859}{409600000} \) |
\( \bigl[a^{2} - a - 5\) , \( -1\) , \( a + 1\) , \( -109399368547725693 a^{2} - 270314409229643934 a - 63038122602220729\) , \( -62593992974445254617256880 a^{2} - 154663216587308206719513082 a - 36067921192472486442537378\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-109399368547725693a^{2}-270314409229643934a-63038122602220729\right){x}-62593992974445254617256880a^{2}-154663216587308206719513082a-36067921192472486442537378$ |
| 10.2-g2 |
10.2-g |
$2$ |
$2$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{9} \cdot 5^{10} \) |
$5.42062$ |
$(-a^2+2a+5), (a^2+3a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.186178965$ |
$36.57429510$ |
1.574611826 |
\( -\frac{1364484982539}{5000000000} a^{2} + \frac{177204090117}{500000000} a + \frac{5147537988191}{2500000000} \) |
\( \bigl[1\) , \( -a^{2} + a + 5\) , \( a + 1\) , \( 6 a^{2} + 17 a + 10\) , \( -1024 a^{2} - 2529 a - 588\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(6a^{2}+17a+10\right){x}-1024a^{2}-2529a-588$ |
| 10.2-h1 |
10.2-h |
$4$ |
$6$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{12} \cdot 5^{3} \) |
$5.42062$ |
$(-a^2+2a+5), (a^2+3a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.613682354$ |
$88.21186794$ |
3.929596663 |
\( \frac{375488569}{512000} a^{2} - \frac{147391607}{51200} a + \frac{773181739}{256000} \) |
\( \bigl[a\) , \( a - 1\) , \( a^{2} - 2 a - 5\) , \( -16 a^{2} + 54 a + 15\) , \( -72 a^{2} + 234 a + 61\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-2a-5\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-16a^{2}+54a+15\right){x}-72a^{2}+234a+61$ |
| 10.2-h2 |
10.2-h |
$4$ |
$6$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{4} \cdot 5 \) |
$5.42062$ |
$(-a^2+2a+5), (a^2+3a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1.841047064$ |
$3.267106220$ |
3.929596663 |
\( \frac{12835591354801}{80} a^{2} - \frac{4177489686911}{8} a - \frac{4792319969389}{40} \) |
\( \bigl[a\) , \( a - 1\) , \( a^{2} - 2 a - 5\) , \( -1351 a^{2} + 4339 a + 1215\) , \( -62826 a^{2} + 201679 a + 56840\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-2a-5\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-1351a^{2}+4339a+1215\right){x}-62826a^{2}+201679a+56840$ |
| 10.2-h3 |
10.2-h |
$4$ |
$6$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{2} \cdot 5^{2} \) |
$5.42062$ |
$(-a^2+2a+5), (a^2+3a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$3.682094128$ |
$1.633553110$ |
3.929596663 |
\( -\frac{10198075083009761729713}{100} a^{2} + \frac{1285682937659047598719}{10} a + \frac{39116339426250361346797}{50} \) |
\( \bigl[a\) , \( 1\) , \( a^{2} - a - 5\) , \( 3750 a^{2} - 4618 a - 29149\) , \( 244493 a^{2} - 307088 a - 1879566\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+{x}^{2}+\left(3750a^{2}-4618a-29149\right){x}+244493a^{2}-307088a-1879566$ |
| 10.2-h4 |
10.2-h |
$4$ |
$6$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{6} \cdot 5^{6} \) |
$5.42062$ |
$(-a^2+2a+5), (a^2+3a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1.227364709$ |
$44.10593397$ |
3.929596663 |
\( -\frac{1243969012313}{1000000} a^{2} + \frac{156765284439}{100000} a + \frac{4773340180597}{500000} \) |
\( \bigl[a\) , \( 1\) , \( a^{2} - a - 5\) , \( 45 a^{2} - 53 a - 359\) , \( 353 a^{2} - 449 a - 2695\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+{x}^{2}+\left(45a^{2}-53a-359\right){x}+353a^{2}-449a-2695$ |
| 10.2-i1 |
10.2-i |
$2$ |
$2$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2 \cdot 5^{2} \) |
$5.42062$ |
$(-a^2+2a+5), (a^2+3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$134.8152815$ |
1.631042186 |
\( -\frac{60852229}{50} a^{2} + \frac{7656927}{5} a + \frac{233220626}{25} \) |
\( \bigl[a^{2} - a - 5\) , \( -1\) , \( 1\) , \( 160342844 a^{2} - 202146049 a - 1230040976\) , \( -2107354169211 a^{2} + 2656765396318 a + 16166184363854\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(160342844a^{2}-202146049a-1230040976\right){x}-2107354169211a^{2}+2656765396318a+16166184363854$ |
| 10.2-i2 |
10.2-i |
$2$ |
$2$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{2} \cdot 5 \) |
$5.42062$ |
$(-a^2+2a+5), (a^2+3a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$134.8152815$ |
1.631042186 |
\( \frac{327761989}{20} a^{2} + \frac{78342985}{2} a + \frac{91023349}{10} \) |
\( \bigl[1\) , \( a^{2} - a - 6\) , \( a^{2} - a - 4\) , \( 227 a^{2} - 281 a - 1759\) , \( -3104 a^{2} + 3905 a + 23836\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(227a^{2}-281a-1759\right){x}-3104a^{2}+3905a+23836$ |
| 10.2-j1 |
10.2-j |
$2$ |
$2$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2 \cdot 5^{6} \) |
$5.42062$ |
$(-a^2+2a+5), (a^2+3a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.368045446$ |
$62.01532252$ |
0.828414671 |
\( \frac{1957141841}{31250} a^{2} - \frac{628333023}{3125} a - \frac{884654029}{15625} \) |
\( \bigl[a\) , \( a^{2} - 3 a - 6\) , \( a^{2} - a - 5\) , \( -7 a^{2} - 22 a + 3\) , \( -591 a^{2} - 1471 a - 354\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a^{2}-3a-6\right){x}^{2}+\left(-7a^{2}-22a+3\right){x}-591a^{2}-1471a-354$ |
| 10.2-j2 |
10.2-j |
$2$ |
$2$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{2} \cdot 5^{3} \) |
$5.42062$ |
$(-a^2+2a+5), (a^2+3a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.184022723$ |
$124.0306450$ |
0.828414671 |
\( \frac{1437769}{500} a^{2} + \frac{701593}{50} a + \frac{4702939}{250} \) |
\( \bigl[a\) , \( -a^{2} + 2 a + 4\) , \( a + 1\) , \( -3903 a^{2} - 9644 a - 2245\) , \( -430856 a^{2} - 1064598 a - 248266\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(-3903a^{2}-9644a-2245\right){x}-430856a^{2}-1064598a-248266$ |
| 14.1-a1 |
14.1-a |
$4$ |
$4$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{3} \cdot 7 \) |
$5.73329$ |
$(-a^2+2a+5), (2a^2-2a-17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$2.427888386$ |
$47.63360733$ |
6.296232762 |
\( -\frac{726461471260619}{56} a^{2} + \frac{457929125527509}{28} a + \frac{2786458559861747}{28} \) |
\( \bigl[a^{2} - a - 5\) , \( -a^{2} + 2 a + 5\) , \( 0\) , \( -31916512226286184155 a^{2} - 78862366955577961691 a - 18390938059922945281\) , \( 319061728826785686677939779482 a^{2} + 788368195178165124089404863735 a + 183849803216049310304110145018\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}={x}^{3}+\left(-a^{2}+2a+5\right){x}^{2}+\left(-31916512226286184155a^{2}-78862366955577961691a-18390938059922945281\right){x}+319061728826785686677939779482a^{2}+788368195178165124089404863735a+183849803216049310304110145018$ |
| 14.1-a2 |
14.1-a |
$4$ |
$4$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{6} \cdot 7^{2} \) |
$5.73329$ |
$(-a^2+2a+5), (2a^2-2a-17)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$1.213944193$ |
$95.26721467$ |
6.296232762 |
\( -\frac{4187324987}{3136} a^{2} + \frac{2639523241}{1568} a + \frac{16063905839}{1568} \) |
\( \bigl[a^{2} - a - 5\) , \( -a^{2} + 2 a + 5\) , \( 0\) , \( -2636108069407231865 a^{2} - 6513547609156898596 a - 1518978636512898936\) , \( 1507660429743447853765201470 a^{2} + 3725271395942473350935520472 a + 868744347196326326014513843\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}={x}^{3}+\left(-a^{2}+2a+5\right){x}^{2}+\left(-2636108069407231865a^{2}-6513547609156898596a-1518978636512898936\right){x}+1507660429743447853765201470a^{2}+3725271395942473350935520472a+868744347196326326014513843$ |
| 14.1-a3 |
14.1-a |
$4$ |
$4$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{12} \cdot 7^{4} \) |
$5.73329$ |
$(-a^2+2a+5), (2a^2-2a-17)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.606972096$ |
$47.63360733$ |
6.296232762 |
\( -\frac{3005262459}{9834496} a^{2} + \frac{1836580073}{4917248} a + \frac{19887116047}{4917248} \) |
\( \bigl[1\) , \( -a^{2} + a + 6\) , \( a + 1\) , \( 2210475474079097494283094344806356 a^{2} + 5461853937773302467215262841037548 a + 1273720550621011687994379989676911\) , \( 37468625579743364108584472899638557317741777727714 a^{2} + 92581058946574790872041826700025168967352508792740 a + 21590177753193886849675157925450811690330449271903\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(2210475474079097494283094344806356a^{2}+5461853937773302467215262841037548a+1273720550621011687994379989676911\right){x}+37468625579743364108584472899638557317741777727714a^{2}+92581058946574790872041826700025168967352508792740a+21590177753193886849675157925450811690330449271903$ |
| 14.1-a4 |
14.1-a |
$4$ |
$4$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{3} \cdot 7 \) |
$5.73329$ |
$(-a^2+2a+5), (2a^2-2a-17)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$2.427888386$ |
$47.63360733$ |
6.296232762 |
\( \frac{1720099}{56} a^{2} - \frac{1613121}{28} a - \frac{547163}{28} \) |
\( \bigl[1\) , \( -a^{2} + 3 a + 6\) , \( a + 1\) , \( -7534 a^{2} - 18616 a - 4332\) , \( -1163795 a^{2} - 2875610 a - 670595\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+3a+6\right){x}^{2}+\left(-7534a^{2}-18616a-4332\right){x}-1163795a^{2}-2875610a-670595$ |
| 14.1-b1 |
14.1-b |
$2$ |
$2$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{14} \cdot 7^{3} \) |
$5.73329$ |
$(-a^2+2a+5), (2a^2-2a-17)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$38.03389938$ |
1.380442047 |
\( \frac{38069978819}{5619712} a^{2} - \frac{22854683393}{2809856} a - \frac{149917740599}{2809856} \) |
\( \bigl[1\) , \( -a^{2} + 3 a + 5\) , \( 0\) , \( -33 a^{2} + 106 a + 34\) , \( 404 a^{2} - 1296 a - 367\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a^{2}+3a+5\right){x}^{2}+\left(-33a^{2}+106a+34\right){x}+404a^{2}-1296a-367$ |
| 14.1-b2 |
14.1-b |
$2$ |
$2$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{7} \cdot 7^{6} \) |
$5.73329$ |
$(-a^2+2a+5), (2a^2-2a-17)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$38.03389938$ |
1.380442047 |
\( -\frac{5481236997119315}{15059072} a^{2} + \frac{3443503730430193}{7529536} a + \frac{21064660537255367}{7529536} \) |
\( \bigl[1\) , \( -a^{2} + 3 a + 5\) , \( 0\) , \( -583 a^{2} + 1881 a + 499\) , \( 19540 a^{2} - 62689 a - 17812\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a^{2}+3a+5\right){x}^{2}+\left(-583a^{2}+1881a+499\right){x}+19540a^{2}-62689a-17812$ |
| 14.1-c1 |
14.1-c |
$1$ |
$1$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( - 2^{6} \cdot 7^{4} \) |
$5.73329$ |
$(-a^2+2a+5), (2a^2-2a-17)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$0.004264629$ |
$243.1248480$ |
1.806338668 |
\( -\frac{87318753813}{153664} a^{2} + \frac{146426106695}{76832} a + \frac{12631948097}{76832} \) |
\( \bigl[a^{2} - 2 a - 4\) , \( -a^{2} + 2 a + 5\) , \( 1\) , \( -9483 a^{2} - 23421 a - 5442\) , \( 1656318 a^{2} + 4092596 a + 954420\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+2a+5\right){x}^{2}+\left(-9483a^{2}-23421a-5442\right){x}+1656318a^{2}+4092596a+954420$ |
| 14.2-a1 |
14.2-a |
$1$ |
$1$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
14.2 |
\( 2 \cdot 7 \) |
\( - 2^{2} \cdot 7^{4} \) |
$5.73329$ |
$(-a^2+2a+5), (a^2-a-9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.078124775$ |
$39.84645642$ |
0.903890456 |
\( -\frac{101541}{196} a^{2} + \frac{226679}{98} a - \frac{30297}{14} \) |
\( \bigl[a^{2} - 2 a - 4\) , \( a^{2} - 2 a - 6\) , \( a + 1\) , \( 2 a^{2} - 8 a + 1\) , \( -a^{2} + 2 a\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2a-6\right){x}^{2}+\left(2a^{2}-8a+1\right){x}-a^{2}+2a$ |
| 14.4-a1 |
14.4-a |
$1$ |
$1$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
14.4 |
\( 2 \cdot 7 \) |
\( - 2^{3} \cdot 7 \) |
$5.73329$ |
$(a), (a^2-a-9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.418101082$ |
$120.9941913$ |
3.672173012 |
\( \frac{6749751}{28} a^{2} - \frac{8502829}{28} a - \frac{12941199}{7} \) |
\( \bigl[1\) , \( a^{2} - a - 4\) , \( 1\) , \( 22 a^{2} - 25 a - 171\) , \( -199 a^{2} + 368 a + 1124\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(22a^{2}-25a-171\right){x}-199a^{2}+368a+1124$ |
| 14.4-b1 |
14.4-b |
$1$ |
$1$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
14.4 |
\( 2 \cdot 7 \) |
\( - 2^{6} \cdot 7 \) |
$5.73329$ |
$(a), (a^2-a-9)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.052900787$ |
$128.8127982$ |
0.989301044 |
\( -\frac{5544639}{56} a^{2} + \frac{4467207}{14} a + \frac{4611283}{56} \) |
\( \bigl[a + 1\) , \( a^{2} - 3 a - 4\) , \( a^{2} - a - 5\) , \( 12 a^{2} - 20 a - 81\) , \( 33 a^{2} - 45 a - 244\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a^{2}-3a-4\right){x}^{2}+\left(12a^{2}-20a-81\right){x}+33a^{2}-45a-244$ |
| 16.1-a1 |
16.1-a |
$1$ |
$1$ |
3.3.1708.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{6} \) |
$5.86231$ |
$(a), (-a^2+2a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.335019088$ |
$25.58931138$ |
2.489232510 |
\( -\frac{9541}{4} a^{2} - \frac{12201}{2} a - \frac{3663}{2} \) |
\( \bigl[a^{2} - 2 a - 4\) , \( a^{2} - a - 4\) , \( a\) , \( 4 a^{2} - 11 a - 4\) , \( 2 a^{2} - 6 a - 2\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(4a^{2}-11a-4\right){x}+2a^{2}-6a-2$ |
*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.
