| 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 |
| 2304.1-a1 |
2304.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{8} \) |
$1.23820$ |
$(a+1), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.337900933$ |
$2.345364298$ |
1.585001572 |
\( \frac{97336}{81} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( -8\) , \( 8 i\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}-8{x}+8i$ |
| 2304.1-a2 |
2304.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{4} \) |
$1.23820$ |
$(a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.675801867$ |
$4.690728597$ |
1.585001572 |
\( \frac{21952}{9} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+2{x}$ |
| 2304.1-a3 |
2304.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{2} \) |
$1.23820$ |
$(a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.337900933$ |
$4.690728597$ |
1.585001572 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -4\) , \( -2\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-4{x}-2$ |
| 2304.1-a4 |
2304.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{2} \) |
$1.23820$ |
$(a+1), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.351603734$ |
$2.345364298$ |
1.585001572 |
\( \frac{7301384}{3} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( 32\) , \( -60 i\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+32{x}-60i$ |
| 2304.1-b1 |
2304.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{4} \) |
$1.23820$ |
$(a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.468762805$ |
1.734381402 |
\( -4048 a - \frac{58624}{9} \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( -6 i + 1\) , \( 5 i - 3\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(-6i+1\right){x}+5i-3$ |
| 2304.1-b2 |
2304.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$1.23820$ |
$(a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$6.937525611$ |
1.734381402 |
\( \frac{6656}{3} a - 1536 \) |
\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( -i + 1\) , \( -i\bigr] \) |
${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+\left(-i+1\right){x}-i$ |
| 2304.1-c1 |
2304.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{16} \) |
$1.23820$ |
$(a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.908836754$ |
1.817673508 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( -16\) , \( 180 i\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}-16{x}+180i$ |
| 2304.1-c2 |
2304.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$1.23820$ |
$(a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$7.270694035$ |
1.817673508 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}-{x}$ |
| 2304.1-c3 |
2304.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{4} \) |
$1.23820$ |
$(a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$3.635347017$ |
1.817673508 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( 4\) , \( -4 i\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+4{x}-4i$ |
| 2304.1-c4 |
2304.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{8} \) |
$1.23820$ |
$(a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.817673508$ |
1.817673508 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( 24\) , \( -36 i\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+24{x}-36i$ |
| 2304.1-c5 |
2304.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{2} \) |
$1.23820$ |
$(a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.817673508$ |
1.817673508 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( -i\) , \( 0\) , \( 64\) , \( -220 i\bigr] \) |
${y}^2={x}^{3}-i{x}^{2}+64{x}-220i$ |
| 2304.1-c6 |
2304.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{4} \) |
$1.23820$ |
$(a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.908836754$ |
1.817673508 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( 384\) , \( -2772 i\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+384{x}-2772i$ |
| 2304.1-d1 |
2304.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{4} \) |
$1.23820$ |
$(a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.468762805$ |
1.734381402 |
\( 4048 a - \frac{58624}{9} \) |
\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( 6 i + 1\) , \( -5 i - 3\bigr] \) |
${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+\left(6i+1\right){x}-5i-3$ |
| 2304.1-d2 |
2304.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$1.23820$ |
$(a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$6.937525611$ |
1.734381402 |
\( -\frac{6656}{3} a - 1536 \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( i + 1\) , \( i\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}+\left(i+1\right){x}+i$ |
*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.
