| 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 |
| 1875.1-a1 |
1875.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{2} \cdot 5^{8} \) |
$1.01847$ |
$(-2a+1), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 5$ |
2Cn, 5B.1.3 |
$1$ |
\( 2 \cdot 3 \) |
$0.025588090$ |
$3.274603091$ |
1.161039937 |
\( -\frac{102400}{3} \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( -8 a + 8\) , \( -7\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(-8a+8\right){x}-7$ |
| 1875.1-a2 |
1875.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{10} \cdot 5^{16} \) |
$1.01847$ |
$(-2a+1), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 5$ |
2Cn, 5B.1.4 |
$1$ |
\( 2 \cdot 3 \) |
$0.127940452$ |
$0.654920618$ |
1.161039937 |
\( \frac{20480}{243} \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( 42 a - 42\) , \( 443\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(42a-42\right){x}+443$ |
| 1875.1-b1 |
1875.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{32} \cdot 5^{14} \) |
$1.01847$ |
$(-2a+1), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1$ |
$0.111785085$ |
1.032626388 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2751\) , \( -104477\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2751{x}-104477$ |
| 1875.1-b2 |
1875.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{2} \cdot 5^{14} \) |
$1.01847$ |
$(-2a+1), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.788561370$ |
1.032626388 |
\( -\frac{1}{15} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 23\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}+23$ |
| 1875.1-b3 |
1875.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{4} \cdot 5^{28} \) |
$1.01847$ |
$(-2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.223570171$ |
1.032626388 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 874\) , \( -5227\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+874{x}-5227$ |
| 1875.1-b4 |
1875.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{8} \cdot 5^{20} \) |
$1.01847$ |
$(-2a+1), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.447140342$ |
1.032626388 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -251\) , \( -727\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-251{x}-727$ |
| 1875.1-b5 |
1875.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{4} \cdot 5^{16} \) |
$1.01847$ |
$(-2a+1), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$0.894280685$ |
1.032626388 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -126\) , \( 523\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-126{x}+523$ |
| 1875.1-b6 |
1875.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{16} \cdot 5^{16} \) |
$1.01847$ |
$(-2a+1), (5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.223570171$ |
1.032626388 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -3376\) , \( -75727\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-3376{x}-75727$ |
| 1875.1-b7 |
1875.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{2} \cdot 5^{14} \) |
$1.01847$ |
$(-2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.447140342$ |
1.032626388 |
\( \frac{56667352321}{15} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2001\) , \( 34273\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2001{x}+34273$ |
| 1875.1-b8 |
1875.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{8} \cdot 5^{14} \) |
$1.01847$ |
$(-2a+1), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.111785085$ |
1.032626388 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -54001\) , \( -4834477\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-54001{x}-4834477$ |
| 1875.1-c1 |
1875.1-c |
$2$ |
$5$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{2} \cdot 5^{20} \) |
$1.01847$ |
$(-2a+1), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 5$ |
2Cn, 5B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$0.654920618$ |
1.512474380 |
\( -\frac{102400}{3} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -208\) , \( -1256\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-208{x}-1256$ |
| 1875.1-c2 |
1875.1-c |
$2$ |
$5$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1875.1 |
\( 3 \cdot 5^{4} \) |
\( 3^{10} \cdot 5^{4} \) |
$1.01847$ |
$(-2a+1), (5)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 5$ |
2Cn, 5B.1.1 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$3.274603091$ |
1.512474380 |
\( \frac{20480}{243} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 2\) , \( 4\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+2{x}+4$ |
*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.
