| 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 |
| 25.2-b1 |
25.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{10} \) |
$0.97888$ |
$(-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$11.99242927$ |
2.447944375 |
\( -\frac{213248}{625} a + \frac{84032}{625} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -2 a + 2\) , \( 5\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a+2\right){x}+5$ |
| 25.2-e1 |
25.2-e |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{10} \) |
$0.97888$ |
$(-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.313341678$ |
0.880457183 |
\( -\frac{213248}{625} a + \frac{84032}{625} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( -56 a + 136\) , \( 302 a - 740\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-56a+136\right){x}+302a-740$ |
| 45.2-b1 |
45.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{6} \cdot 5^{4} \) |
$1.13383$ |
$(a+3), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$6.778545114$ |
2.767329454 |
\( -\frac{213248}{625} a + \frac{84032}{625} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -a + 3\) , \( -a + 1\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-a+3\right){x}-a+1$ |
| 45.2-e1 |
45.2-e |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
45.2 |
\( 3^{2} \cdot 5 \) |
\( 3^{6} \cdot 5^{4} \) |
$1.13383$ |
$(a+3), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.155438783$ |
$12.71842363$ |
0.807080863 |
\( -\frac{213248}{625} a + \frac{84032}{625} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -8 a - 21\) , \( 28 a + 68\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-8a-21\right){x}+28a+68$ |
| 125.1-b1 |
125.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
125.1 |
\( 5^{3} \) |
\( 5^{10} \) |
$1.46377$ |
$(-a-1), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.047616179$ |
$11.99242927$ |
0.932494071 |
\( -\frac{213248}{625} a + \frac{84032}{625} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( -4 a - 6\) , \( 7 a + 18\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-4a-6\right){x}+7a+18$ |
| 125.1-d1 |
125.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
125.1 |
\( 5^{3} \) |
\( 5^{10} \) |
$1.46377$ |
$(-a-1), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.313341678$ |
1.760914366 |
\( -\frac{213248}{625} a + \frac{84032}{625} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -12 a + 28\) , \( 6 a - 15\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-12a+28\right){x}+6a-15$ |
| 400.2-i1 |
400.2-i |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
400.2 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{10} \) |
$1.95776$ |
$(-a+2), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.156670839$ |
0.440228591 |
\( -\frac{213248}{625} a + \frac{84032}{625} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -222 a + 544\) , \( 2416 a - 5918\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-222a+544\right){x}+2416a-5918$ |
| 400.2-m1 |
400.2-m |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
400.2 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{10} \) |
$1.95776$ |
$(-a+2), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.996214637$ |
1.223972187 |
\( -\frac{213248}{625} a + \frac{84032}{625} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -4 a + 2\) , \( 2 a + 12\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-4a+2\right){x}+2a+12$ |
| 720.2-h1 |
720.2-h |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
720.2 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{12} \cdot 3^{6} \cdot 5^{4} \) |
$2.26766$ |
$(-a+2), (a+3), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.105287680$ |
$3.389272557$ |
2.913012303 |
\( -\frac{213248}{625} a + \frac{84032}{625} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -6 a + 15\) , \( -15 a + 36\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-6a+15\right){x}-15a+36$ |
| 720.2-j1 |
720.2-j |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
720.2 |
\( 2^{4} \cdot 3^{2} \cdot 5 \) |
\( 2^{12} \cdot 3^{6} \cdot 5^{4} \) |
$2.26766$ |
$(-a+2), (a+3), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$6.359211816$ |
2.596137352 |
\( -\frac{213248}{625} a + \frac{84032}{625} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -34 a - 81\) , \( 341 a + 836\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-34a-81\right){x}+341a+836$ |
*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.
