| 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 |
| 27104.6-a1 |
27104.6-a |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.6 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{12} \cdot 7 \cdot 11^{2} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.136882134$ |
$3.595509661$ |
2.976310195 |
\( -\frac{151031}{112} a + \frac{523157}{56} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( a + 4\) , \( 3 a - 7\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(a+4\right){x}+3a-7$ |
| 27104.6-a2 |
27104.6-a |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.6 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{20} \cdot 7^{3} \cdot 11^{2} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.410646403$ |
$1.198503220$ |
2.976310195 |
\( \frac{24989591975}{200704} a + \frac{42797130331}{100352} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 46 a + 54\) , \( -131 a + 333\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(46a+54\right){x}-131a+333$ |
| 27104.6-b1 |
27104.6-b |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.6 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{10} \cdot 7^{5} \cdot 11^{8} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$0.693813856$ |
1.048947953 |
\( -\frac{680543}{1372} a + \frac{159053}{686} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -53 a + 38\) , \( 257 a - 282\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-53a+38\right){x}+257a-282$ |
| 27104.6-c1 |
27104.6-c |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.6 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{48} \cdot 7^{2} \cdot 11^{6} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{6} \) |
$4.166277711$ |
$0.131974098$ |
3.325124285 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -2217 a - 5797\) , \( -107002 a - 149730\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-2217a-5797\right){x}-107002a-149730$ |
| 27104.6-c2 |
27104.6-c |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.6 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{27} \cdot 7^{3} \cdot 11^{6} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \) |
$2.777518474$ |
$0.395922296$ |
3.325124285 |
\( \frac{10538337875}{200704} a - \frac{36575498625}{200704} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 550 a - 51\) , \( -1911 a - 6734\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(550a-51\right){x}-1911a-6734$ |
| 27104.6-c3 |
27104.6-c |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.6 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{27} \cdot 7^{3} \cdot 11^{6} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \) |
$2.777518474$ |
$0.395922296$ |
3.325124285 |
\( -\frac{10538337875}{200704} a - \frac{13018580375}{100352} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( -260 a + 808\) , \( -4400 a - 2848\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-260a+808\right){x}-4400a-2848$ |
| 27104.6-c4 |
27104.6-c |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.6 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{17} \cdot 7 \cdot 11^{6} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.925839491$ |
$1.187766888$ |
3.325124285 |
\( \frac{831875}{112} a - \frac{499125}{56} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 15 a + 38\) , \( 105 a - 150\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(15a+38\right){x}+105a-150$ |
| 27104.6-c5 |
27104.6-c |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.6 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{17} \cdot 7 \cdot 11^{6} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.925839491$ |
$1.187766888$ |
3.325124285 |
\( -\frac{831875}{112} a - \frac{166375}{112} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 15 a + 39\) , \( -86 a + 124\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(15a+39\right){x}-86a+124$ |
| 27104.6-c6 |
27104.6-c |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.6 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{16} \cdot 7^{2} \cdot 11^{6} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{6} \) |
$0.462919745$ |
$1.187766888$ |
3.325124285 |
\( -\frac{15625}{28} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -7 a - 17\) , \( 38 a + 62\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-7a-17\right){x}+38a+62$ |
| 27104.6-c7 |
27104.6-c |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.6 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{24} \cdot 7^{6} \cdot 11^{6} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3Cs |
$1$ |
\( 2^{6} \) |
$1.388759237$ |
$0.395922296$ |
3.325124285 |
\( \frac{9938375}{21952} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 58 a + 153\) , \( -777 a - 1176\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(58a+153\right){x}-777a-1176$ |
| 27104.6-c8 |
27104.6-c |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.6 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{57} \cdot 7 \cdot 11^{6} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$8.332555422$ |
$0.131974098$ |
3.325124285 |
\( \frac{70135314719125}{481036337152} a + \frac{288417990127625}{481036337152} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -1525 a + 479\) , \( -11576 a - 35288\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-1525a+479\right){x}-11576a-35288$ |
| 27104.6-c9 |
27104.6-c |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.6 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{57} \cdot 7 \cdot 11^{6} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$8.332555422$ |
$0.131974098$ |
3.325124285 |
\( -\frac{70135314719125}{481036337152} a + \frac{179276652423375}{240518168576} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 905 a - 2102\) , \( -25735 a - 16502\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(905a-2102\right){x}-25735a-16502$ |
| 27104.6-c10 |
27104.6-c |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.6 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{18} \cdot 7^{12} \cdot 11^{6} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{4} \) |
$2.777518474$ |
$0.197961148$ |
3.325124285 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -462 a - 1207\) , \( -8257 a - 11208\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-462a-1207\right){x}-8257a-11208$ |
| 27104.6-c11 |
27104.6-c |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.6 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{14} \cdot 7^{4} \cdot 11^{6} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$0.925839491$ |
$0.593883444$ |
3.325124285 |
\( \frac{128787625}{98} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -137 a - 357\) , \( 1668 a + 2538\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-137a-357\right){x}+1668a+2538$ |
| 27104.6-c12 |
27104.6-c |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.6 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{30} \cdot 7^{4} \cdot 11^{6} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$8.332555422$ |
$0.065987049$ |
3.325124285 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -35497 a - 92837\) , \( -6857722 a - 9723106\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-35497a-92837\right){x}-6857722a-9723106$ |
| 27104.6-d1 |
27104.6-d |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.6 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{28} \cdot 7^{3} \cdot 11^{8} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 3 \cdot 5 \) |
$0.227832765$ |
$0.326594068$ |
6.749734578 |
\( -\frac{58211797249}{51380224} a + \frac{99605592787}{25690112} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 363 a + 34\) , \( a - 3434\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(363a+34\right){x}+a-3434$ |
| 27104.6-e1 |
27104.6-e |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.6 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{14} \cdot 7^{3} \cdot 11^{10} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.504539270$ |
4.576750071 |
\( \frac{1896471}{3136} a - \frac{1539061}{1568} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -97 a - 36\) , \( -812 a + 651\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-97a-36\right){x}-812a+651$ |
| 27104.6-e2 |
27104.6-e |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.6 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{10} \cdot 7^{9} \cdot 11^{10} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$9$ |
\( 2^{2} \) |
$1$ |
$0.168179756$ |
4.576750071 |
\( \frac{3507393849}{67228} a + \frac{11298024197}{33614} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -717 a + 5044\) , \( -90932 a + 6059\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-717a+5044\right){x}-90932a+6059$ |
| 27104.6-f1 |
27104.6-f |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.6 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{22} \cdot 7 \cdot 11^{8} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \cdot 5 \) |
$0.236904872$ |
$0.670889151$ |
7.208700609 |
\( -\frac{386167}{7168} a + \frac{1476373}{3584} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 49 a - 28\) , \( -144 a + 383\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(49a-28\right){x}-144a+383$ |
| 27104.6-g1 |
27104.6-g |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.6 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{8} \cdot 7^{4} \cdot 11^{9} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.651481602$ |
3.939790407 |
\( \frac{4807755}{784} a - \frac{8042193}{392} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 71 a - 198\) , \( -538 a + 1151\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(71a-198\right){x}-538a+1151$ |
| 27104.6-g2 |
27104.6-g |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
27104.6 |
\( 2^{5} \cdot 7 \cdot 11^{2} \) |
\( 2^{16} \cdot 7^{2} \cdot 11^{9} \) |
$3.03351$ |
$(a), (-a+1), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.651481602$ |
3.939790407 |
\( \frac{783675}{1792} a - \frac{511137}{896} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 41 a - 81\) , \( -252 a + 568\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(41a-81\right){x}-252a+568$ |
*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.
