| 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 |
| 23104.2-a1 |
23104.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
23104.2 |
\( 2^{6} \cdot 19^{2} \) |
\( 2^{16} \cdot 19^{2} \) |
$1.90819$ |
$(-5a+3), (-5a+2), (2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.040898934$ |
$3.397222379$ |
2.566996744 |
\( -\frac{1024}{19} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 3\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-{x}+3$ |
| 2888.1-a1 |
2888.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2888.1 |
\( 2^{3} \cdot 19^{2} \) |
\( 2^{4} \cdot 19^{2} \) |
$1.31014$ |
$(a+1), (19)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2 \) |
$0.065414869$ |
$6.794444758$ |
1.777830871 |
\( -\frac{1024}{19} \) |
\( \bigl[0\) , \( i\) , \( i + 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(i+1\right){y}={x}^{3}+i{x}^{2}$ |
| 23104.4-a1 |
23104.4-a |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23104.4 |
\( 2^{6} \cdot 19^{2} \) |
\( 2^{16} \cdot 19^{2} \) |
$2.91480$ |
$(a), (-a+1), (19)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2^{4} \) |
$0.035079726$ |
$3.397222379$ |
5.765555048 |
\( -\frac{1024}{19} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 3\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-{x}+3$ |
| 2888.2-a1 |
2888.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2888.2 |
\( 2^{3} \cdot 19^{2} \) |
\( 2^{4} \cdot 19^{2} \) |
$1.85282$ |
$(a), (-3a+1), (3a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2 \) |
$0.065414869$ |
$6.794444758$ |
1.257116264 |
\( -\frac{1024}{19} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( 0\) , \( 0\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}$ |
| 23104.1-a1 |
23104.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
23104.1 |
\( 2^{6} \cdot 19^{2} \) |
\( 2^{16} \cdot 19^{2} \) |
$3.65390$ |
$(2), (19)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.065414869$ |
$3.397222379$ |
1.072072352 |
\( -\frac{1024}{19} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 3\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-{x}+3$ |
| 1216.1-a1 |
1216.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-19}) \) |
$2$ |
$[0, 1]$ |
1216.1 |
\( 2^{6} \cdot 19 \) |
\( 2^{16} \cdot 19^{2} \) |
$2.30011$ |
$(-2a+1), (2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cn |
$1$ |
\( 2^{3} \) |
$0.076308808$ |
$3.397222379$ |
3.806289563 |
\( -\frac{1024}{19} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 3\bigr] \) |
${y}^2={x}^3+{x}^2-{x}+3$ |
| 2888.1-d1 |
2888.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2888.1 |
\( 2^{3} \cdot 19^{2} \) |
\( 2^{4} \cdot 19^{2} \) |
$1.85282$ |
$(a), (19)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2 \) |
$0.065414869$ |
$26.58148262$ |
2.459068793 |
\( -\frac{1024}{19} \) |
\( \bigl[0\) , \( -1\) , \( a\) , \( 0\) , \( 0\bigr] \) |
${y}^2+a{y}={x}^{3}-{x}^{2}$ |
| 2888.1-d1 |
2888.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2888.1 |
\( 2^{3} \cdot 19^{2} \) |
\( 2^{4} \cdot 19^{2} \) |
$2.26923$ |
$(a+1), (19)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2 \) |
$0.055727156$ |
$26.58148262$ |
3.420939919 |
\( -\frac{1024}{19} \) |
\( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( -2 a - 1\) , \( 6 a + 11\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a-1\right){x}+6a+11$ |
| 152.1-d1 |
152.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{19}) \) |
$2$ |
$[2, 0]$ |
152.1 |
\( 2^{3} \cdot 19 \) |
\( 2^{4} \cdot 19^{2} \) |
$2.73531$ |
$(-3a+13), (a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.065414869$ |
$26.58148262$ |
1.595654537 |
\( -\frac{1024}{19} \) |
\( \bigl[0\) , \( 1\) , \( a + 1\) , \( 4420 a - 19266\) , \( -1918755 a + 8363652\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(4420a-19266\right){x}-1918755a+8363652$ |
*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.
