| 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 |
| 63.1-a1 |
63.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( 3^{2} \cdot 7^{16} \) |
$2.20912$ |
$(a+3), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$3.651881942$ |
1.664682285 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -307 a - 1182\) , \( 16747 a + 65111\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-307a-1182\right){x}+16747a+65111$ |
| 63.1-a2 |
63.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( 3^{4} \cdot 7^{2} \) |
$2.20912$ |
$(a+3), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$14.60752776$ |
1.664682285 |
\( \frac{103823}{63} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 8 a + 43\) , \( 17 a + 74\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(8a+43\right){x}+17a+74$ |
| 63.1-a3 |
63.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( 3^{8} \cdot 7^{4} \) |
$2.20912$ |
$(a+3), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$14.60752776$ |
1.664682285 |
\( \frac{7189057}{3969} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -37 a - 132\) , \( 7 a + 35\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-37a-132\right){x}+7a+35$ |
| 63.1-a4 |
63.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( 3^{16} \cdot 7^{2} \) |
$2.20912$ |
$(a+3), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$3.651881942$ |
1.664682285 |
\( \frac{6570725617}{45927} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -352 a - 1357\) , \( -7903 a - 30716\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-352a-1357\right){x}-7903a-30716$ |
| 63.1-a5 |
63.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( 3^{4} \cdot 7^{8} \) |
$2.20912$ |
$(a+3), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$14.60752776$ |
1.664682285 |
\( \frac{13027640977}{21609} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -442 a - 1707\) , \( 9997 a + 38870\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-442a-1707\right){x}+9997a+38870$ |
| 63.1-a6 |
63.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( 3^{2} \cdot 7^{4} \) |
$2.20912$ |
$(a+3), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$14.60752776$ |
1.664682285 |
\( \frac{53297461115137}{147} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 7057 a - 34489\) , \( -667087 a + 3260376\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(7057a-34489\right){x}-667087a+3260376$ |
| 63.1-b1 |
63.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( 3^{2} \cdot 7^{16} \) |
$2.20912$ |
$(a+3), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$26.22178070$ |
$0.814020435$ |
2.432495953 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -34\) , \( -217\bigr] \) |
${y}^2+{x}{y}={x}^{3}-34{x}-217$ |
| 63.1-b2 |
63.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( 3^{4} \cdot 7^{2} \) |
$2.20912$ |
$(a+3), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.277722588$ |
$13.02432697$ |
2.432495953 |
\( \frac{103823}{63} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}$ |
| 63.1-b3 |
63.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( 3^{8} \cdot 7^{4} \) |
$2.20912$ |
$(a+3), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$6.555445177$ |
$13.02432697$ |
2.432495953 |
\( \frac{7189057}{3969} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -4\) , \( -1\bigr] \) |
${y}^2+{x}{y}={x}^{3}-4{x}-1$ |
| 63.1-b4 |
63.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( 3^{16} \cdot 7^{2} \) |
$2.20912$ |
$(a+3), (3)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$3.277722588$ |
$13.02432697$ |
2.432495953 |
\( \frac{6570725617}{45927} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -39\) , \( 90\bigr] \) |
${y}^2+{x}{y}={x}^{3}-39{x}+90$ |
| 63.1-b5 |
63.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( 3^{4} \cdot 7^{8} \) |
$2.20912$ |
$(a+3), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$13.11089035$ |
$3.256081743$ |
2.432495953 |
\( \frac{13027640977}{21609} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -49\) , \( -136\bigr] \) |
${y}^2+{x}{y}={x}^{3}-49{x}-136$ |
| 63.1-b6 |
63.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{77}) \) |
$2$ |
$[2, 0]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( 3^{2} \cdot 7^{4} \) |
$2.20912$ |
$(a+3), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$26.22178070$ |
$0.814020435$ |
2.432495953 |
\( \frac{53297461115137}{147} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -784\) , \( -8515\bigr] \) |
${y}^2+{x}{y}={x}^{3}-784{x}-8515$ |
*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.
