| 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 |
| 6.1-a4 |
6.1-a |
$8$ |
$28$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{4} \cdot 3 \) |
$0.67072$ |
$(2,a), (3,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.2.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$9.972901485$ |
1.039746854 |
\( \frac{9841}{48} a + \frac{43625}{48} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( a - 2\) , \( -1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(a+1\right){x}^2+\left(a-2\right){x}-1$ |
| 144.1-a4 |
144.1-a |
$8$ |
$28$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{28} \cdot 3^{7} \) |
$1.48454$ |
$(2,a), (3,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 7$ |
2B, 7B |
$1$ |
\( 2^{3} \) |
$0.307123774$ |
$2.878928678$ |
1.474926613 |
\( \frac{9841}{48} a + \frac{43625}{48} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -7 a + 15\) , \( -8 a - 28\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-a{x}^2+\left(-7a+15\right){x}-8a-28$ |
| 162.3-a4 |
162.3-a |
$8$ |
$28$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
162.3 |
\( 2 \cdot 3^{4} \) |
\( 2^{4} \cdot 3^{13} \) |
$1.52891$ |
$(2,a), (3,a), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 7$ |
2B, 7B |
$1$ |
\( 2^{4} \) |
$0.107018254$ |
$3.324300495$ |
1.186900192 |
\( \frac{9841}{48} a + \frac{43625}{48} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -2 a\) , \( 4\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^3-{x}^2-2a{x}+4$ |
| 192.1-a4 |
192.1-a |
$8$ |
$28$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
192.1 |
\( 2^{6} \cdot 3 \) |
\( 2^{22} \cdot 3 \) |
$1.59525$ |
$(2,a), (3,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 7$ |
2B, 7B |
$1$ |
\( 2^{2} \) |
$0.441143926$ |
$3.525953134$ |
1.297337325 |
\( \frac{9841}{48} a + \frac{43625}{48} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 2\) , \( -a + 1\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+2{x}-a+1$ |
| 288.13-c4 |
288.13-c |
$8$ |
$28$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
288.13 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{7} \) |
$1.76543$ |
$(2,a), (2,a+1), (3,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 7$ |
2B, 7B |
$1$ |
\( 2^{5} \) |
$1$ |
$2.878928678$ |
2.401192506 |
\( \frac{9841}{48} a + \frac{43625}{48} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -2 a - 2\) , \( -a + 7\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(-2a-2\right){x}-a+7$ |
| 384.13-c4 |
384.13-c |
$8$ |
$28$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
384.13 |
\( 2^{7} \cdot 3 \) |
\( 2^{22} \cdot 3 \) |
$1.89708$ |
$(2,a), (2,a+1), (3,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 7$ |
2B, 7B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.525953134$ |
1.470424103 |
\( \frac{9841}{48} a + \frac{43625}{48} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -a + 6\) , \( -a - 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-a{x}^2+\left(-a+6\right){x}-a-2$ |
| 432.3-b4 |
432.3-b |
$8$ |
$28$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
432.3 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{16} \cdot 3^{7} \) |
$1.95377$ |
$(2,a), (3,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 7$ |
2B, 7B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.878928678$ |
2.401192506 |
\( \frac{9841}{48} a + \frac{43625}{48} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -a + 5\) , \( 5\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+\left(a+1\right){x}^2+\left(-a+5\right){x}+5$ |
| 576.1-c4 |
576.1-c |
$8$ |
$28$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{34} \cdot 3^{7} \) |
$2.09946$ |
$(2,a), (3,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 7$ |
2B, 7B |
$1$ |
\( 2^{3} \) |
$1.128075471$ |
$2.035709991$ |
3.830717567 |
\( \frac{9841}{48} a + \frac{43625}{48} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 13 a + 18\) , \( -26 a - 44\bigr] \) |
${y}^2={x}^3+\left(13a+18\right){x}-26a-44$ |
| 768.9-b4 |
768.9-b |
$8$ |
$28$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
768.9 |
\( 2^{8} \cdot 3 \) |
\( 2^{28} \cdot 3 \) |
$2.25602$ |
$(2,a), (2,a+1), (3,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 7$ |
2B, 7B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.493225371$ |
2.079493709 |
\( \frac{9841}{48} a + \frac{43625}{48} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -3 a - 2\) , \( 0\bigr] \) |
${y}^2={x}^3+\left(-a+1\right){x}^2+\left(-3a-2\right){x}$ |
| 864.19-a4 |
864.19-a |
$8$ |
$28$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
864.19 |
\( 2^{5} \cdot 3^{3} \) |
\( 2^{28} \cdot 3^{7} \) |
$2.32344$ |
$(2,a), (2,a+1), (3,a), (3,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 7$ |
2B, 7B |
$1$ |
\( 2^{3} \) |
$0.477253099$ |
$2.878928678$ |
2.291953130 |
\( \frac{9841}{48} a + \frac{43625}{48} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -4 a - 20\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a+1\right){x}^2+\left(-4a-20\right){x}$ |
| 1014.1-b4 |
1014.1-b |
$8$ |
$28$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
1014.1 |
\( 2 \cdot 3 \cdot 13^{2} \) |
\( 2^{16} \cdot 3 \cdot 13^{6} \) |
$2.41831$ |
$(2,a), (3,a), (13,a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 7$ |
2B, 7B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.765985205$ |
1.153495568 |
\( \frac{9841}{48} a + \frac{43625}{48} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 7 a + 7\) , \( 8 a + 8\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-a{x}^2+\left(7a+7\right){x}+8a+8$ |
| 1014.3-a4 |
1014.3-a |
$8$ |
$28$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
1014.3 |
\( 2 \cdot 3 \cdot 13^{2} \) |
\( 2^{16} \cdot 3 \cdot 13^{6} \) |
$2.41831$ |
$(2,a), (3,a), (13,a+8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 7$ |
2B, 7B |
$1$ |
\( 2^{3} \) |
$0.906963380$ |
$2.765985205$ |
4.184712962 |
\( \frac{9841}{48} a + \frac{43625}{48} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 9 a - 5\) , \( -13 a - 12\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(a+1\right){x}^2+\left(9a-5\right){x}-13a-12$ |
| 1152.19-b4 |
1152.19-b |
$8$ |
$28$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
1152.19 |
\( 2^{7} \cdot 3^{2} \) |
\( 2^{34} \cdot 3^{7} \) |
$2.49670$ |
$(2,a), (2,a+1), (3,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 7$ |
2B, 7B |
$1$ |
\( 2^{4} \) |
$0.371930884$ |
$2.035709991$ |
2.526005057 |
\( \frac{9841}{48} a + \frac{43625}{48} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -17 a + 18\) , \( 33 a + 70\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3-{x}^2+\left(-17a+18\right){x}+33a+70$ |
| 1728.3-d4 |
1728.3-d |
$8$ |
$28$ |
\(\Q(\sqrt{-23}) \) |
$2$ |
$[0, 1]$ |
1728.3 |
\( 2^{6} \cdot 3^{3} \) |
\( 2^{34} \cdot 3^{7} \) |
$2.76305$ |
$(2,a), (3,a), (3,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 7$ |
2B, 7B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.035709991$ |
1.697899503 |
\( \frac{9841}{48} a + \frac{43625}{48} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -12 a - 24\) , \( -39 a + 102\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(a+1\right){x}^2+\left(-12a-24\right){x}-39a+102$ |
*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.
