| 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 |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
400.1 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{12} \) |
$0.69217$ |
$(2), (5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$1.070515942$ |
0.618062667 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -36 a + 36\) , \( -140\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-36a+36\right){x}-140$ |
| 6400.1-h1 |
6400.1-h |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
6400.1 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{12} \) |
$1.38434$ |
$(2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$1.070515942$ |
1.854188003 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -36\) , \( 140\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-36{x}+140$ |
| 10000.1-a1 |
10000.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
10000.1 |
\( 2^{4} \cdot 5^{4} \) |
\( 2^{16} \cdot 5^{24} \) |
$1.54774$ |
$(2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{2} \cdot 3 \) |
$1.957327600$ |
$0.214103188$ |
2.903402684 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -908\) , \( -15688\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-908{x}-15688$ |
| 57600.1-g1 |
57600.1-g |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{6} \cdot 5^{12} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1.293210583$ |
$0.618062667$ |
3.691740124 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 109\) , \( -731 a + 420\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+109\right){x}-731a+420$ |
| 57600.1-l1 |
57600.1-l |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{6} \cdot 5^{12} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1.293210583$ |
$0.618062667$ |
3.691740124 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 110 a - 109\) , \( 731 a - 311\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(110a-109\right){x}+731a-311$ |
| 67600.1-a1 |
67600.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
67600.1 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{16} \cdot 5^{12} \cdot 13^{6} \) |
$2.49566$ |
$(-4a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$3.953390776$ |
$0.296907701$ |
5.421513801 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 545 a - 254\) , \( -4787 a - 2090\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(545a-254\right){x}-4787a-2090$ |
| 67600.3-a1 |
67600.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
67600.3 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{16} \cdot 5^{12} \cdot 13^{6} \) |
$2.49566$ |
$(4a-3), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$3.953390776$ |
$0.296907701$ |
5.421513801 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -545 a + 291\) , \( 4787 a - 6877\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-545a+291\right){x}+4787a-6877$ |
| 102400.1-a1 |
102400.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
102400.1 |
\( 2^{12} \cdot 5^{2} \) |
\( 2^{28} \cdot 5^{12} \) |
$2.76869$ |
$(2), (5)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.269748285$ |
$0.535257971$ |
4.001312284 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 145 a\) , \( 975\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+145a{x}+975$ |
| 102400.1-t1 |
102400.1-t |
$4$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
102400.1 |
\( 2^{12} \cdot 5^{2} \) |
\( 2^{28} \cdot 5^{12} \) |
$2.76869$ |
$(2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.535257971$ |
3.708376006 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -145\) , \( -975\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-145{x}-975$ |
*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.
