| 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 |
| 36.1-a1 |
36.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{40} \cdot 3^{2} \) |
$0.78920$ |
$(-a), (-a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$25$ |
\( 2 \) |
$1$ |
$0.308426902$ |
1.069277895 |
\( -\frac{4395631034341}{3145728} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 1023 a - 2390\) , \( 24243 a - 55924\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(1023a-2390\right){x}+24243a-55924$ |
| 36.1-a2 |
36.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{10} \) |
$0.78920$ |
$(-a), (-a+1), (2)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2 \cdot 5^{2} \) |
$1$ |
$7.710672559$ |
1.069277895 |
\( \frac{5735339}{3888} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -12 a + 25\) , \( -12 a + 26\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-12a+25\right){x}-12a+26$ |
| 36.1-a3 |
36.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{20} \) |
$0.78920$ |
$(-a), (-a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 2^{3} \cdot 5^{2} \) |
$1$ |
$7.710672559$ |
1.069277895 |
\( \frac{476379541}{236196} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 48 a - 115\) , \( -96 a + 218\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(48a-115\right){x}-96a+218$ |
| 36.1-a4 |
36.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{25} \) |
$0.78920$ |
$(-a), (-a+1), (2)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2^{2} \cdot 5^{2} \) |
$1$ |
$3.855336279$ |
1.069277895 |
\( -\frac{1025795879759761}{3486784401} a + \frac{5304841542920801}{6973568802} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -420 a - 565\) , \( -6327 a - 8227\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-420a-565\right){x}-6327a-8227$ |
| 36.1-a5 |
36.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{2} \cdot 3^{25} \) |
$0.78920$ |
$(-a), (-a+1), (2)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2^{2} \cdot 5^{2} \) |
$1$ |
$3.855336279$ |
1.069277895 |
\( \frac{1025795879759761}{3486784401} a + \frac{1084416594467093}{2324522934} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 418 a - 985\) , \( 6326 a - 14554\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(418a-985\right){x}+6326a-14554$ |
| 36.1-a6 |
36.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{5} \) |
$0.78920$ |
$(-a), (-a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$25$ |
\( 2^{2} \) |
$1$ |
$0.154213451$ |
1.069277895 |
\( -\frac{1373276865151726904870180471}{1296} a + \frac{2108232339288241560240379517}{864} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -14305 a - 26645\) , \( -1473236 a - 2202528\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-14305a-26645\right){x}-1473236a-2202528$ |
| 36.1-a7 |
36.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{4} \) |
$0.78920$ |
$(-a), (-a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2Cs, 5B.1.2 |
$25$ |
\( 2^{3} \) |
$1$ |
$0.308426902$ |
1.069277895 |
\( \frac{18013780041269221}{9216} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 16383 a - 38230\) , \( 1551027 a - 3576436\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(16383a-38230\right){x}+1551027a-3576436$ |
| 36.1-a8 |
36.1-a |
$8$ |
$20$ |
\(\Q(\sqrt{13}) \) |
$2$ |
$[2, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{5} \) |
$0.78920$ |
$(-a), (-a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$25$ |
\( 2^{2} \) |
$1$ |
$0.154213451$ |
1.069277895 |
\( \frac{1373276865151726904870180471}{1296} a + \frac{3578143287561270870980777609}{2592} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 14303 a - 40950\) , \( 1473235 a - 3675764\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(14303a-40950\right){x}+1473235a-3675764$ |
*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.
