| 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 |
| 400.1-a1 |
400.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{2}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
400.1 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{6} \) |
$7.55886$ |
$(1/2a^3-2a), (-a^2+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 3^{2} \) |
$0.842895411$ |
$12.56968764$ |
2.383859709 |
\( \frac{85201943541088}{25} a^{2} - \frac{65088492979664}{25} \) |
\( \bigl[a\) , \( -\frac{1}{2} a^{2}\) , \( 0\) , \( \frac{25}{2} a^{2} - 89\) , \( 29 a^{2} - 187\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-\frac{1}{2}a^{2}{x}^{2}+\left(\frac{25}{2}a^{2}-89\right){x}+29a^{2}-187$ |
| 400.1-a2 |
400.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{2}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
400.1 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{2} \) |
$7.55886$ |
$(1/2a^3-2a), (-a^2+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$0.280965137$ |
$1018.144699$ |
2.383859709 |
\( \frac{6676448}{5} a^{2} - \frac{4972624}{5} \) |
\( \bigl[a\) , \( \frac{1}{2} a^{2} - 1\) , \( a\) , \( -\frac{1}{2} a^{2} - 2\) , \( -1\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(\frac{1}{2}a^{2}-1\right){x}^{2}+\left(-\frac{1}{2}a^{2}-2\right){x}-1$ |
| 400.1-a3 |
400.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{2}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
400.1 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{24} \) |
$7.55886$ |
$(1/2a^3-2a), (-a^2+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.842895411$ |
$3.142421912$ |
2.383859709 |
\( -\frac{20720464}{15625} \) |
\( \bigl[\frac{1}{2} a^{3} - 2 a\) , \( 0\) , \( \frac{1}{2} a^{3} - 2 a\) , \( -10\) , \( -18\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-2a\right){x}{y}+\left(\frac{1}{2}a^{3}-2a\right){y}={x}^{3}-10{x}-18$ |
| 400.1-a4 |
400.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{2}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
400.1 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{8} \) |
$7.55886$ |
$(1/2a^3-2a), (-a^2+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.280965137$ |
$254.5361748$ |
2.383859709 |
\( \frac{21296}{25} \) |
\( \bigl[\frac{1}{2} a^{3} - 2 a\) , \( 0\) , \( \frac{1}{2} a^{3} - 2 a\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-2a\right){x}{y}+\left(\frac{1}{2}a^{3}-2a\right){y}={x}^{3}$ |
| 400.1-a5 |
400.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{2}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
400.1 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{4} \) |
$7.55886$ |
$(1/2a^3-2a), (-a^2+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.561930274$ |
$1018.144699$ |
2.383859709 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-{x}$ |
| 400.1-a6 |
400.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{2}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
400.1 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{12} \) |
$7.55886$ |
$(1/2a^3-2a), (-a^2+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1.685790823$ |
$12.56968764$ |
2.383859709 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -41\) , \( -116\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-41{x}-116$ |
| 400.1-a7 |
400.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{2}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
400.1 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{2} \) |
$7.55886$ |
$(1/2a^3-2a), (-a^2+3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$0.280965137$ |
$1018.144699$ |
2.383859709 |
\( -\frac{6676448}{5} a^{2} + \frac{35086064}{5} \) |
\( \bigl[\frac{1}{2} a^{3} - a\) , \( 1\) , \( a\) , \( a^{2} - 5\) , \( -a^{2} + 3\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(a^{2}-5\right){x}-a^{2}+3$ |
| 400.1-a8 |
400.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{2}, \sqrt{5})\) |
$4$ |
$[4, 0]$ |
400.1 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{6} \) |
$7.55886$ |
$(1/2a^3-2a), (-a^2+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 3^{2} \) |
$0.842895411$ |
$12.56968764$ |
2.383859709 |
\( -\frac{85201943541088}{25} a^{2} + \frac{446123168266864}{25} \) |
\( \bigl[\frac{1}{2} a^{3} - a\) , \( -\frac{1}{2} a^{2} + 2\) , \( \frac{1}{2} a^{3} - a\) , \( -\frac{27}{2} a^{2} - 13\) , \( -42 a^{2} - 27\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-a\right){x}{y}+\left(\frac{1}{2}a^{3}-a\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+2\right){x}^{2}+\left(-\frac{27}{2}a^{2}-13\right){x}-42a^{2}-27$ |
*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.
