| 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-a4 |
400.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
400.1 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{6} \) |
$0.69217$ |
$(2), (5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 3^{2} \) |
$1$ |
$2.141031885$ |
0.618062667 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -41 a + 41\) , \( -116\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-41a+41\right){x}-116$ |
| 6400.1-h4 |
6400.1-h |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
6400.1 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{6} \) |
$1.38434$ |
$(2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 3 \) |
$1$ |
$2.141031885$ |
1.854188003 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -41\) , \( 116\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-41{x}+116$ |
| 10000.1-a4 |
10000.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
10000.1 |
\( 2^{4} \cdot 5^{4} \) |
\( 2^{8} \cdot 5^{18} \) |
$1.54774$ |
$(2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.978663800$ |
$0.428206377$ |
2.903402684 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -1033\) , \( -12438\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-1033{x}-12438$ |
| 57600.1-g4 |
57600.1-g |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{6} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2 \) |
$2.586421166$ |
$1.236125335$ |
3.691740124 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 124\) , \( -572 a + 348\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+124\right){x}-572a+348$ |
| 57600.1-l4 |
57600.1-l |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{6} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2 \) |
$2.586421166$ |
$1.236125335$ |
3.691740124 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 125 a - 124\) , \( 572 a - 224\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(125a-124\right){x}+572a-224$ |
| 67600.1-a4 |
67600.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
67600.1 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{6} \cdot 13^{6} \) |
$2.49566$ |
$(-4a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2 \) |
$7.906781553$ |
$0.593815403$ |
5.421513801 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 620 a - 289\) , \( -3888 a - 1642\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(620a-289\right){x}-3888a-1642$ |
| 67600.3-a4 |
67600.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
67600.3 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{6} \cdot 13^{6} \) |
$2.49566$ |
$(4a-3), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2 \) |
$7.906781553$ |
$0.593815403$ |
5.421513801 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -620 a + 331\) , \( 3888 a - 5530\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-620a+331\right){x}+3888a-5530$ |
| 102400.1-a4 |
102400.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
102400.1 |
\( 2^{12} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{6} \) |
$2.76869$ |
$(2), (5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.269748285$ |
$1.070515942$ |
4.001312284 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 165 a\) , \( 763\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+165a{x}+763$ |
| 102400.1-t4 |
102400.1-t |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
102400.1 |
\( 2^{12} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{6} \) |
$2.76869$ |
$(2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.070515942$ |
3.708376006 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -165\) , \( -763\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-165{x}-763$ |
*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.
