| 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 |
| 23104.1-a1 |
23104.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
23104.1 |
\( 2^{6} \cdot 19^{2} \) |
\( 2^{12} \cdot 19^{2} \) |
$2.20338$ |
$(a+1), (19)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.058229357$ |
$4.183446943$ |
3.897590849 |
\( -\frac{13824}{19} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2\) , \( -2 i\bigr] \) |
${y}^2={x}^{3}+2{x}-2i$ |
| 23104.1-b1 |
23104.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
23104.1 |
\( 2^{6} \cdot 19^{2} \) |
\( 2^{6} \cdot 19^{2} \) |
$2.20338$ |
$(a+1), (19)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 1 \) |
$0.314996586$ |
$5.963775842$ |
3.757138071 |
\( \frac{27000}{19} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( -2\) , \( -i\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}-2{x}-i$ |
| 23104.1-c1 |
23104.1-c |
$3$ |
$25$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
23104.1 |
\( 2^{6} \cdot 19^{2} \) |
\( 2^{12} \cdot 19^{2} \) |
$2.20338$ |
$(a+1), (19)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2 \) |
$1.806491839$ |
$0.603483608$ |
4.360752859 |
\( -\frac{5698354821120}{19} a - \frac{4288599378432}{19} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1080 i - 1186\) , \( 22126 i - 11040\bigr] \) |
${y}^2={x}^{3}+\left(1080i-1186\right){x}+22126i-11040$ |
| 23104.1-c2 |
23104.1-c |
$3$ |
$25$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
23104.1 |
\( 2^{6} \cdot 19^{2} \) |
\( 2^{12} \cdot 19^{2} \) |
$2.20338$ |
$(a+1), (19)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2 \) |
$1.806491839$ |
$0.603483608$ |
4.360752859 |
\( \frac{5698354821120}{19} a - \frac{4288599378432}{19} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1080 i - 1186\) , \( -22126 i - 11040\bigr] \) |
${y}^2={x}^{3}+\left(-1080i-1186\right){x}-22126i-11040$ |
| 23104.1-c3 |
23104.1-c |
$3$ |
$25$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
23104.1 |
\( 2^{6} \cdot 19^{2} \) |
\( 2^{12} \cdot 19^{10} \) |
$2.20338$ |
$(a+1), (19)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5Cs |
$1$ |
\( 2 \cdot 5 \) |
$0.361298367$ |
$0.603483608$ |
4.360752859 |
\( -\frac{4741632}{2476099} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 14\) , \( 606 i\bigr] \) |
${y}^2={x}^{3}+14{x}+606i$ |
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*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.
