| 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 |
| 38332.4-a1 |
38332.4-a |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
38332.4 |
\( 2^{2} \cdot 7 \cdot 37^{2} \) |
\( 2^{11} \cdot 7 \cdot 37^{2} \) |
$3.30809$ |
$(a), (-a+1), (-2a+1), (-4a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.221487060$ |
$3.261382188$ |
2.184193057 |
\( -\frac{3456035}{1792} a - \frac{199223}{896} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 4\) , \( 2 a\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+4{x}+2a$ |
| 38332.4-a2 |
38332.4-a |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
38332.4 |
\( 2^{2} \cdot 7 \cdot 37^{2} \) |
\( 2^{25} \cdot 7^{3} \cdot 37^{2} \) |
$3.30809$ |
$(a), (-a+1), (-2a+1), (-4a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.664461182$ |
$1.087127396$ |
2.184193057 |
\( \frac{462220013915}{822083584} a + \frac{446117919999}{411041792} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -5 a - 36\) , \( -30 a - 34\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-5a-36\right){x}-30a-34$ |
| 38332.4-b1 |
38332.4-b |
$6$ |
$18$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
38332.4 |
\( 2^{2} \cdot 7 \cdot 37^{2} \) |
\( 2^{19} \cdot 7^{9} \cdot 37^{8} \) |
$3.30809$ |
$(a), (-a+1), (-2a+1), (-4a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$18.88059431$ |
$0.045462986$ |
2.595461512 |
\( \frac{74070862058537322875}{6031614410752} a - \frac{36764016519943734625}{3015807205376} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -66691 a - 33284\) , \( -10508028 a + 2598270\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-66691a-33284\right){x}-10508028a+2598270$ |
| 38332.4-b2 |
38332.4-b |
$6$ |
$18$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
38332.4 |
\( 2^{2} \cdot 7 \cdot 37^{2} \) |
\( 2^{9} \cdot 7^{6} \cdot 37^{9} \) |
$3.30809$ |
$(a), (-a+1), (-2a+1), (-4a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{4} \) |
$3.146765719$ |
$0.136388960$ |
2.595461512 |
\( -\frac{165270320824375}{1111934656} a - \frac{545259680442875}{1111934656} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 1465 a + 6845\) , \( 188111 a - 188573\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(1465a+6845\right){x}+188111a-188573$ |
| 38332.4-b3 |
38332.4-b |
$6$ |
$18$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
38332.4 |
\( 2^{2} \cdot 7 \cdot 37^{2} \) |
\( 2^{11} \cdot 7 \cdot 37^{8} \) |
$3.30809$ |
$(a), (-a+1), (-2a+1), (-4a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$2.097843812$ |
$0.409166882$ |
2.595461512 |
\( \frac{627024389875}{4906496} a - \frac{701112294625}{4906496} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 509 a + 6\) , \( -1284 a - 6292\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(509a+6\right){x}-1284a-6292$ |
| 38332.4-b4 |
38332.4-b |
$6$ |
$18$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
38332.4 |
\( 2^{2} \cdot 7 \cdot 37^{2} \) |
\( 2^{11} \cdot 7^{18} \cdot 37^{7} \) |
$3.30809$ |
$(a), (-a+1), (-2a+1), (-4a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$9.440297157$ |
$0.045462986$ |
2.595461512 |
\( -\frac{1954310051858125}{764458731008} a - \frac{145455576119625}{382229365504} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -13390 a + 26755\) , \( -458172 a - 1565079\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-13390a+26755\right){x}-458172a-1565079$ |
| 38332.4-b5 |
38332.4-b |
$6$ |
$18$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
38332.4 |
\( 2^{2} \cdot 7 \cdot 37^{2} \) |
\( 2^{19} \cdot 7^{2} \cdot 37^{7} \) |
$3.30809$ |
$(a), (-a+1), (-2a+1), (-4a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1.048921906$ |
$0.409166882$ |
2.595461512 |
\( -\frac{4248788375}{67895296} a + \frac{17730430125}{67895296} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -10 a - 145\) , \( 1262 a - 1271\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-10a-145\right){x}+1262a-1271$ |
| 38332.4-b6 |
38332.4-b |
$6$ |
$18$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
38332.4 |
\( 2^{2} \cdot 7 \cdot 37^{2} \) |
\( 2^{9} \cdot 7^{3} \cdot 37^{12} \) |
$3.30809$ |
$(a), (-a+1), (-2a+1), (-4a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \) |
$6.293531438$ |
$0.136388960$ |
2.595461512 |
\( \frac{3195609870461125}{8046118018624} a + \frac{1372681753816125}{4023059009312} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -1466 a + 856\) , \( -9660 a - 37484\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1466a+856\right){x}-9660a-37484$ |
| 38332.4-c1 |
38332.4-c |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
38332.4 |
\( 2^{2} \cdot 7 \cdot 37^{2} \) |
\( 2^{36} \cdot 7^{2} \cdot 37^{6} \) |
$3.30809$ |
$(a), (-a+1), (-2a+1), (-4a+5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$1$ |
$0.143917690$ |
1.958247865 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 4092 a + 1193\) , \( -3495 a + 198341\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(4092a+1193\right){x}-3495a+198341$ |
| 38332.4-c2 |
38332.4-c |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
38332.4 |
\( 2^{2} \cdot 7 \cdot 37^{2} \) |
\( 2^{15} \cdot 7^{3} \cdot 37^{6} \) |
$3.30809$ |
$(a), (-a+1), (-2a+1), (-4a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.431753071$ |
1.958247865 |
\( \frac{10538337875}{200704} a - \frac{36575498625}{200704} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -458 a + 437\) , \( -1528 a + 6857\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-458a+437\right){x}-1528a+6857$ |
| 38332.4-c3 |
38332.4-c |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
38332.4 |
\( 2^{2} \cdot 7 \cdot 37^{2} \) |
\( 2^{15} \cdot 7^{3} \cdot 37^{6} \) |
$3.30809$ |
$(a), (-a+1), (-2a+1), (-4a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.431753071$ |
1.958247865 |
\( -\frac{10538337875}{200704} a - \frac{13018580375}{100352} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( -78 a - 593\) , \( 1115 a + 5473\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-78a-593\right){x}+1115a+5473$ |
| 38332.4-c4 |
38332.4-c |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
38332.4 |
\( 2^{2} \cdot 7 \cdot 37^{2} \) |
\( 2^{5} \cdot 7 \cdot 37^{6} \) |
$3.30809$ |
$(a), (-a+1), (-2a+1), (-4a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.295259214$ |
1.958247865 |
\( \frac{831875}{112} a - \frac{499125}{56} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( -28 a - 8\) , \( -86 a + 46\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-28a-8\right){x}-86a+46$ |
| 38332.4-c5 |
38332.4-c |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
38332.4 |
\( 2^{2} \cdot 7 \cdot 37^{2} \) |
\( 2^{5} \cdot 7 \cdot 37^{6} \) |
$3.30809$ |
$(a), (-a+1), (-2a+1), (-4a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.295259214$ |
1.958247865 |
\( -\frac{831875}{112} a - \frac{166375}{112} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -28 a - 8\) , \( 71 a - 35\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-28a-8\right){x}+71a-35$ |
| 38332.4-c6 |
38332.4-c |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
38332.4 |
\( 2^{2} \cdot 7 \cdot 37^{2} \) |
\( 2^{4} \cdot 7^{2} \cdot 37^{6} \) |
$3.30809$ |
$(a), (-a+1), (-2a+1), (-4a+5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.295259214$ |
1.958247865 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 12 a + 3\) , \( a - 57\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(12a+3\right){x}+a-57$ |
| 38332.4-c7 |
38332.4-c |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
38332.4 |
\( 2^{2} \cdot 7 \cdot 37^{2} \) |
\( 2^{12} \cdot 7^{6} \cdot 37^{6} \) |
$3.30809$ |
$(a), (-a+1), (-2a+1), (-4a+5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2Cs, 3Cs |
$1$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$0.431753071$ |
1.958247865 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -108 a - 32\) , \( -23 a + 1305\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-108a-32\right){x}-23a+1305$ |
| 38332.4-c8 |
38332.4-c |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
38332.4 |
\( 2^{2} \cdot 7 \cdot 37^{2} \) |
\( 2^{45} \cdot 7 \cdot 37^{6} \) |
$3.30809$ |
$(a), (-a+1), (-2a+1), (-4a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$0.143917690$ |
1.958247865 |
\( \frac{70135314719125}{481036337152} a + \frac{288417990127625}{481036337152} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( 1142 a - 1378\) , \( -6585 a + 35443\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(1142a-1378\right){x}-6585a+35443$ |
| 38332.4-c9 |
38332.4-c |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
38332.4 |
\( 2^{2} \cdot 7 \cdot 37^{2} \) |
\( 2^{45} \cdot 7 \cdot 37^{6} \) |
$3.30809$ |
$(a), (-a+1), (-2a+1), (-4a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$0.143917690$ |
1.958247865 |
\( -\frac{70135314719125}{481036337152} a + \frac{179276652423375}{240518168576} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( 2 a + 1712\) , \( 5898 a + 30084\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(2a+1712\right){x}+5898a+30084$ |
| 38332.4-c10 |
38332.4-c |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
38332.4 |
\( 2^{2} \cdot 7 \cdot 37^{2} \) |
\( 2^{6} \cdot 7^{12} \cdot 37^{6} \) |
$3.30809$ |
$(a), (-a+1), (-2a+1), (-4a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$4$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.215876535$ |
1.958247865 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 852 a + 248\) , \( -279 a + 15833\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(852a+248\right){x}-279a+15833$ |
| 38332.4-c11 |
38332.4-c |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
38332.4 |
\( 2^{2} \cdot 7 \cdot 37^{2} \) |
\( 2^{2} \cdot 7^{4} \cdot 37^{6} \) |
$3.30809$ |
$(a), (-a+1), (-2a+1), (-4a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.647629607$ |
1.958247865 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 252 a + 73\) , \( 49 a - 2781\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(252a+73\right){x}+49a-2781$ |
| 38332.4-c12 |
38332.4-c |
$12$ |
$36$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
38332.4 |
\( 2^{2} \cdot 7 \cdot 37^{2} \) |
\( 2^{18} \cdot 7^{4} \cdot 37^{6} \) |
$3.30809$ |
$(a), (-a+1), (-2a+1), (-4a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.071958845$ |
1.958247865 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 65532 a + 19113\) , \( -220583 a + 12518085\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(65532a+19113\right){x}-220583a+12518085$ |
| 38332.4-d1 |
38332.4-d |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
38332.4 |
\( 2^{2} \cdot 7 \cdot 37^{2} \) |
\( 2^{11} \cdot 7 \cdot 37^{8} \) |
$3.30809$ |
$(a), (-a+1), (-2a+1), (-4a+5)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$3.349328439$ |
$0.536167929$ |
5.429996343 |
\( -\frac{3456035}{1792} a - \frac{199223}{896} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -131 a + 19\) , \( -857 a + 607\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-131a+19\right){x}-857a+607$ |
| 38332.4-d2 |
38332.4-d |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
38332.4 |
\( 2^{2} \cdot 7 \cdot 37^{2} \) |
\( 2^{25} \cdot 7^{3} \cdot 37^{8} \) |
$3.30809$ |
$(a), (-a+1), (-2a+1), (-4a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1.116442813$ |
$0.178722643$ |
5.429996343 |
\( \frac{462220013915}{822083584} a + \frac{446117919999}{411041792} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( 984 a + 59\) , \( 9568 a + 4161\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(984a+59\right){x}+9568a+4161$ |
*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.
