| 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 |
| 126.1-a1 |
126.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( 2^{16} \cdot 3^{4} \cdot 7^{2} \) |
$2.24040$ |
$(-a+4), (-2a+7), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$2.283039317$ |
$2.486887276$ |
6.069675380 |
\( -\frac{7189057}{16128} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -483 a - 1801\) , \( -25124 a - 94009\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-483a-1801\right){x}-25124a-94009$ |
| 126.1-a2 |
126.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( 2^{2} \cdot 3^{32} \cdot 7^{4} \) |
$2.24040$ |
$(-a+4), (-2a+7), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1.141519658$ |
$0.621721819$ |
6.069675380 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 46317 a + 173309\) , \( -3968216 a - 14847709\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(46317a+173309\right){x}-3968216a-14847709$ |
| 126.1-a3 |
126.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$2.24040$ |
$(-a+4), (-2a+7), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$0.570759829$ |
$2.486887276$ |
6.069675380 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -12483 a - 46701\) , \( -532140 a - 1991089\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-12483a-46701\right){x}-532140a-1991089$ |
| 126.1-a4 |
126.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( 2^{2} \cdot 3^{8} \cdot 7^{16} \) |
$2.24040$ |
$(-a+4), (-2a+7), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1.141519658$ |
$2.486887276$ |
6.069675380 |
\( \frac{84448510979617}{933897762} \) |
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 109683 a - 410391\) , \( -37770816 a + 141325451\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(109683a-410391\right){x}-37770816a+141325451$ |
| 126.1-a5 |
126.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( 2^{8} \cdot 3^{8} \cdot 7^{4} \) |
$2.24040$ |
$(-a+4), (-2a+7), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1.141519658$ |
$2.486887276$ |
6.069675380 |
\( \frac{65597103937}{63504} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -10083 a - 37721\) , \( -1075140 a - 4022809\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-10083a-37721\right){x}-1075140a-4022809$ |
| 126.1-a6 |
126.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( 2^{4} \cdot 3^{4} \cdot 7^{2} \) |
$2.24040$ |
$(-a+4), (-2a+7), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$2.283039317$ |
$0.621721819$ |
6.069675380 |
\( \frac{268498407453697}{252} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -161283 a - 603461\) , \( -68359644 a - 255778369\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-161283a-603461\right){x}-68359644a-255778369$ |
| 126.1-b1 |
126.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( 2^{16} \cdot 3^{4} \cdot 7^{2} \) |
$2.24040$ |
$(-a+4), (-2a+7), (3)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$12.07873502$ |
1.614088862 |
\( -\frac{7189057}{16128} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -4\) , \( 5\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-4{x}+5$ |
| 126.1-b2 |
126.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( 2^{2} \cdot 3^{32} \cdot 7^{4} \) |
$2.24040$ |
$(-a+4), (-2a+7), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.754920939$ |
1.614088862 |
\( \frac{6359387729183}{4218578658} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 386\) , \( 1277\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+386{x}+1277$ |
| 126.1-b3 |
126.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \) |
$2.24040$ |
$(-a+4), (-2a+7), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$3.019683757$ |
1.614088862 |
\( \frac{124475734657}{63011844} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-104{x}+101$ |
| 126.1-b4 |
126.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( 2^{2} \cdot 3^{8} \cdot 7^{16} \) |
$2.24040$ |
$(-a+4), (-2a+7), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.754920939$ |
1.614088862 |
\( \frac{84448510979617}{933897762} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -914\) , \( -10915\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-914{x}-10915$ |
| 126.1-b5 |
126.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( 2^{8} \cdot 3^{8} \cdot 7^{4} \) |
$2.24040$ |
$(-a+4), (-2a+7), (3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$12.07873502$ |
1.614088862 |
\( \frac{65597103937}{63504} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -84\) , \( 261\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-84{x}+261$ |
| 126.1-b6 |
126.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
126.1 |
\( 2 \cdot 3^{2} \cdot 7 \) |
\( 2^{4} \cdot 3^{4} \cdot 7^{2} \) |
$2.24040$ |
$(-a+4), (-2a+7), (3)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$12.07873502$ |
1.614088862 |
\( \frac{268498407453697}{252} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -1344\) , \( 18405\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-1344{x}+18405$ |
*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.
