| 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 |
$4$ |
$10$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{8} \) |
$8.39127$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.1.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$1962.456482$ |
1.308304321 |
\( \frac{131872229}{18} \) |
\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{10}{7}\) , \( \frac{2}{7} a^{3} - \frac{3}{7} a^{2} - \frac{12}{7} a + \frac{3}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{10}{7}\) , \( \frac{20}{7} a^{3} - \frac{30}{7} a^{2} - \frac{120}{7} a - \frac{47}{7}\) , \( -\frac{62}{7} a^{3} + \frac{93}{7} a^{2} + \frac{372}{7} a + \frac{47}{7}\bigr] \) |
${y}^2+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{12}{7}a-\frac{10}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{12}{7}a-\frac{10}{7}\right){y}={x}^{3}+\left(\frac{2}{7}a^{3}-\frac{3}{7}a^{2}-\frac{12}{7}a+\frac{3}{7}\right){x}^{2}+\left(\frac{20}{7}a^{3}-\frac{30}{7}a^{2}-\frac{120}{7}a-\frac{47}{7}\right){x}-\frac{62}{7}a^{3}+\frac{93}{7}a^{2}+\frac{372}{7}a+\frac{47}{7}$ |
| 36.1-a2 |
36.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{40} \cdot 3^{20} \) |
$8.39127$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.1.4[2] |
$25$ |
\( 2^{2} \) |
$1$ |
$3.139930371$ |
1.308304321 |
\( -\frac{19465109}{248832} \) |
\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{10}{7}\) , \( \frac{2}{7} a^{3} - \frac{3}{7} a^{2} - \frac{12}{7} a + \frac{3}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{10}{7}\) , \( \frac{10}{7} a^{3} - \frac{15}{7} a^{2} - \frac{60}{7} a - \frac{27}{7}\) , \( \frac{80}{7} a^{3} - \frac{120}{7} a^{2} - \frac{480}{7} a - \frac{104}{7}\bigr] \) |
${y}^2+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{12}{7}a-\frac{10}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{12}{7}a-\frac{10}{7}\right){y}={x}^{3}+\left(\frac{2}{7}a^{3}-\frac{3}{7}a^{2}-\frac{12}{7}a+\frac{3}{7}\right){x}^{2}+\left(\frac{10}{7}a^{3}-\frac{15}{7}a^{2}-\frac{60}{7}a-\frac{27}{7}\right){x}+\frac{80}{7}a^{3}-\frac{120}{7}a^{2}-\frac{480}{7}a-\frac{104}{7}$ |
| 36.1-a3 |
36.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{4} \) |
$8.39127$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.1.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$1962.456482$ |
1.308304321 |
\( -\frac{24389}{12} \) |
\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{10}{7}\) , \( \frac{2}{7} a^{3} - \frac{3}{7} a^{2} - \frac{12}{7} a + \frac{3}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{10}{7}\) , \( -1\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{3}{7}\bigr] \) |
${y}^2+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{12}{7}a-\frac{10}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{12}{7}a-\frac{10}{7}\right){y}={x}^{3}+\left(\frac{2}{7}a^{3}-\frac{3}{7}a^{2}-\frac{12}{7}a+\frac{3}{7}\right){x}^{2}-{x}-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{12}{7}a-\frac{3}{7}$ |
| 36.1-a4 |
36.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{40} \) |
$8.39127$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.1.4[2] |
$25$ |
\( 2^{2} \) |
$1$ |
$3.139930371$ |
1.308304321 |
\( \frac{502270291349}{1889568} \) |
\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{10}{7}\) , \( \frac{2}{7} a^{3} - \frac{3}{7} a^{2} - \frac{12}{7} a + \frac{3}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{12}{7} a - \frac{10}{7}\) , \( \frac{330}{7} a^{3} - \frac{495}{7} a^{2} - \frac{1980}{7} a - \frac{667}{7}\) , \( \frac{2704}{7} a^{3} - \frac{4056}{7} a^{2} - \frac{16224}{7} a - \frac{3336}{7}\bigr] \) |
${y}^2+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{12}{7}a-\frac{10}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{12}{7}a-\frac{10}{7}\right){y}={x}^{3}+\left(\frac{2}{7}a^{3}-\frac{3}{7}a^{2}-\frac{12}{7}a+\frac{3}{7}\right){x}^{2}+\left(\frac{330}{7}a^{3}-\frac{495}{7}a^{2}-\frac{1980}{7}a-\frac{667}{7}\right){x}+\frac{2704}{7}a^{3}-\frac{4056}{7}a^{2}-\frac{16224}{7}a-\frac{3336}{7}$ |
| 36.1-b1 |
36.1-b |
$4$ |
$10$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{8} \) |
$8.39127$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$48.99321078$ |
0.816553513 |
\( \frac{131872229}{18} \) |
\( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} + \frac{6}{7} a - \frac{19}{7}\) , \( \frac{2}{7} a^{3} - \frac{3}{7} a^{2} - \frac{12}{7} a + \frac{10}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{10}{7}\) , \( \frac{22}{7} a^{3} - \frac{33}{7} a^{2} - \frac{132}{7} a - \frac{30}{7}\) , \( 6 a^{3} - 9 a^{2} - 36 a - 11\bigr] \) |
${y}^2+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}+\frac{6}{7}a-\frac{19}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{10}{7}\right){y}={x}^{3}+\left(\frac{2}{7}a^{3}-\frac{3}{7}a^{2}-\frac{12}{7}a+\frac{10}{7}\right){x}^{2}+\left(\frac{22}{7}a^{3}-\frac{33}{7}a^{2}-\frac{132}{7}a-\frac{30}{7}\right){x}+6a^{3}-9a^{2}-36a-11$ |
| 36.1-b2 |
36.1-b |
$4$ |
$10$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{40} \cdot 3^{20} \) |
$8.39127$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$48.99321078$ |
0.816553513 |
\( -\frac{19465109}{248832} \) |
\( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} + \frac{6}{7} a - \frac{19}{7}\) , \( \frac{2}{7} a^{3} - \frac{3}{7} a^{2} - \frac{12}{7} a + \frac{10}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{10}{7}\) , \( \frac{12}{7} a^{3} - \frac{18}{7} a^{2} - \frac{72}{7} a - \frac{10}{7}\) , \( -\frac{90}{7} a^{3} + \frac{135}{7} a^{2} + \frac{540}{7} a + \frac{89}{7}\bigr] \) |
${y}^2+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}+\frac{6}{7}a-\frac{19}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{10}{7}\right){y}={x}^{3}+\left(\frac{2}{7}a^{3}-\frac{3}{7}a^{2}-\frac{12}{7}a+\frac{10}{7}\right){x}^{2}+\left(\frac{12}{7}a^{3}-\frac{18}{7}a^{2}-\frac{72}{7}a-\frac{10}{7}\right){x}-\frac{90}{7}a^{3}+\frac{135}{7}a^{2}+\frac{540}{7}a+\frac{89}{7}$ |
| 36.1-b3 |
36.1-b |
$4$ |
$10$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{4} \) |
$8.39127$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$48.99321078$ |
0.816553513 |
\( -\frac{24389}{12} \) |
\( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} + \frac{6}{7} a - \frac{19}{7}\) , \( \frac{2}{7} a^{3} - \frac{3}{7} a^{2} - \frac{12}{7} a + \frac{10}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{10}{7}\) , \( \frac{2}{7} a^{3} - \frac{3}{7} a^{2} - \frac{12}{7} a + \frac{10}{7}\) , \( \frac{2}{7} a^{3} - \frac{3}{7} a^{2} - \frac{12}{7} a + \frac{3}{7}\bigr] \) |
${y}^2+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}+\frac{6}{7}a-\frac{19}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{10}{7}\right){y}={x}^{3}+\left(\frac{2}{7}a^{3}-\frac{3}{7}a^{2}-\frac{12}{7}a+\frac{10}{7}\right){x}^{2}+\left(\frac{2}{7}a^{3}-\frac{3}{7}a^{2}-\frac{12}{7}a+\frac{10}{7}\right){x}+\frac{2}{7}a^{3}-\frac{3}{7}a^{2}-\frac{12}{7}a+\frac{3}{7}$ |
| 36.1-b4 |
36.1-b |
$4$ |
$10$ |
\(\Q(\sqrt{3}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{40} \) |
$8.39127$ |
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 5$ |
2B, 5B.4.1[2] |
$1$ |
\( 2^{2} \) |
$1$ |
$48.99321078$ |
0.816553513 |
\( \frac{502270291349}{1889568} \) |
\( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} + \frac{6}{7} a - \frac{19}{7}\) , \( \frac{2}{7} a^{3} - \frac{3}{7} a^{2} - \frac{12}{7} a + \frac{10}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{10}{7}\) , \( \frac{332}{7} a^{3} - \frac{498}{7} a^{2} - \frac{1992}{7} a - \frac{650}{7}\) , \( -\frac{3034}{7} a^{3} + \frac{4551}{7} a^{2} + \frac{18204}{7} a + \frac{2841}{7}\bigr] \) |
${y}^2+\left(-\frac{1}{7}a^{3}+\frac{5}{7}a^{2}+\frac{6}{7}a-\frac{19}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{10}{7}\right){y}={x}^{3}+\left(\frac{2}{7}a^{3}-\frac{3}{7}a^{2}-\frac{12}{7}a+\frac{10}{7}\right){x}^{2}+\left(\frac{332}{7}a^{3}-\frac{498}{7}a^{2}-\frac{1992}{7}a-\frac{650}{7}\right){x}-\frac{3034}{7}a^{3}+\frac{4551}{7}a^{2}+\frac{18204}{7}a+\frac{2841}{7}$ |
*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.
