| 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-a6 |
63.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( 3^{2} \cdot 7 \) |
$0.66607$ |
$(-2a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$6.896615437$ |
0.325834452 |
\( \frac{2940226}{21} a + \frac{2980207}{21} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( -2 a + 1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-2a+1\right){x}$ |
| 567.1-a6 |
567.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( 3^{14} \cdot 7 \) |
$1.15367$ |
$(-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.659627205$ |
$2.298871812$ |
2.292578873 |
\( \frac{2940226}{21} a + \frac{2980207}{21} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -18 a + 15\) , \( -10 a + 46\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-18a+15\right){x}-10a+46$ |
| 4032.1-c6 |
4032.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.1 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{18} \cdot 3^{2} \cdot 7 \) |
$1.88394$ |
$(a), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.438321771$ |
1.843198006 |
\( \frac{2940226}{21} a + \frac{2980207}{21} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -6 a + 24\) , \( -21 a - 18\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-6a+24\right){x}-21a-18$ |
| 4032.7-c6 |
4032.7-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.7 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{18} \cdot 3^{2} \cdot 7 \) |
$1.88394$ |
$(-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.438321771$ |
1.843198006 |
\( \frac{2940226}{21} a + \frac{2980207}{21} \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -13 a - 10\) , \( 16 a + 13\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-13a-10\right){x}+16a+13$ |
| 7056.1-c6 |
7056.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7056.1 |
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{2} \cdot 7^{7} \) |
$2.16684$ |
$(a), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.303337809$ |
1.970461553 |
\( \frac{2940226}{21} a + \frac{2980207}{21} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 20 a + 62\) , \( 168 a - 229\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(20a+62\right){x}+168a-229$ |
| 7056.5-c6 |
7056.5-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7056.5 |
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{2} \cdot 7^{7} \) |
$2.16684$ |
$(-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.303337809$ |
1.970461553 |
\( \frac{2940226}{21} a + \frac{2980207}{21} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -7 a - 74\) , \( -77 a - 197\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-7a-74\right){x}-77a-197$ |
| 16128.5-i4 |
16128.5-i |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{24} \cdot 3^{2} \cdot 7 \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.746299208$ |
$1.724153859$ |
3.890719903 |
\( \frac{2940226}{21} a + \frac{2980207}{21} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -31 a + 26\) , \( -22 a + 88\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-31a+26\right){x}-22a+88$ |
| 28224.1-d4 |
28224.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28224.1 |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{18} \cdot 3^{2} \cdot 7^{7} \) |
$3.06438$ |
$(a), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.485887490$ |
$0.921599003$ |
2.070326753 |
\( \frac{2940226}{21} a + \frac{2980207}{21} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 40 a - 162\) , \( 275 a - 795\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(40a-162\right){x}+275a-795$ |
| 28224.7-d4 |
28224.7-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28224.7 |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{18} \cdot 3^{2} \cdot 7^{7} \) |
$3.06438$ |
$(-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.371471872$ |
$0.921599003$ |
2.070326753 |
\( \frac{2940226}{21} a + \frac{2980207}{21} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 86 a + 58\) , \( 274 a - 858\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(86a+58\right){x}+274a-858$ |
| 36288.1-c4 |
36288.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.1 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{18} \cdot 3^{14} \cdot 7 \) |
$3.26308$ |
$(a), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.812773923$ |
1.228798671 |
\( \frac{2940226}{21} a + \frac{2980207}{21} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -51 a + 210\) , \( 672 a + 64\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-51a+210\right){x}+672a+64$ |
| 36288.7-c4 |
36288.7-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.7 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{18} \cdot 3^{14} \cdot 7 \) |
$3.26308$ |
$(-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.812773923$ |
1.228798671 |
\( \frac{2940226}{21} a + \frac{2980207}{21} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -111 a - 76\) , \( -833 a + 90\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-111a-76\right){x}-833a+90$ |
| 39375.1-d4 |
39375.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39375.1 |
\( 3^{2} \cdot 5^{4} \cdot 7 \) |
\( 3^{2} \cdot 5^{12} \cdot 7 \) |
$3.33037$ |
$(-2a+1), (3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$7.725929285$ |
$1.379323087$ |
8.055596601 |
\( \frac{2940226}{21} a + \frac{2980207}{21} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -51 a + 41\) , \( 49 a - 246\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-51a+41\right){x}+49a-246$ |
*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.
