| 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-CMa1 |
2304.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{6} \) |
$1.07231$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$5.108115717$ |
1.474585992 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -1\bigr] \) |
${y}^2={x}^{3}-1$ |
| 2304.1-CMa2 |
2304.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{6} \) |
$1.07231$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-12$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$2.554057858$ |
1.474585992 |
\( 54000 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -15 a + 15\) , \( -22\bigr] \) |
${y}^2={x}^{3}+\left(-15a+15\right){x}-22$ |
| 2304.1-a1 |
2304.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{7} \) |
$1.07231$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2.098868579$ |
1.211782339 |
\( -\frac{73696}{3} a - \frac{550672}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 16 a - 32\) , \( -44 a + 48\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(16a-32\right){x}-44a+48$ |
| 2304.1-a2 |
2304.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{7} \) |
$1.07231$ |
$(-2a+1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.098868579$ |
1.211782339 |
\( \frac{73696}{3} a - \frac{624368}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -14 a - 17\) , \( -59 a - 21\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-14a-17\right){x}-59a-21$ |
| 2304.1-a3 |
2304.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{22} \) |
$1.07231$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.524717144$ |
1.211782339 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a - 47\) , \( 1033 a - 540\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a-47\right){x}+1033a-540$ |
| 2304.1-a4 |
2304.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \) |
$1.07231$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$4.197737158$ |
1.211782339 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a - 2\) , \( -2 a\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a-2\right){x}-2a$ |
| 2304.1-a5 |
2304.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{10} \) |
$1.07231$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$2.098868579$ |
1.211782339 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 13\) , \( -11 a + 12\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+13\right){x}-11a+12$ |
| 2304.1-a6 |
2304.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{14} \) |
$1.07231$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.049434289$ |
1.211782339 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 73\) , \( 289 a - 108\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+73\right){x}+289a-108$ |
| 2304.1-a7 |
2304.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{8} \) |
$1.07231$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.049434289$ |
1.211782339 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 193\) , \( -1127 a + 660\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+193\right){x}-1127a+660$ |
| 2304.1-a8 |
2304.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{10} \) |
$1.07231$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.524717144$ |
1.211782339 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 1153\) , \( 17785 a - 8316\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+1153\right){x}+17785a-8316$ |
| 2304.1-b1 |
2304.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{7} \) |
$1.07231$ |
$(-2a+1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.098868579$ |
1.211782339 |
\( -\frac{73696}{3} a - \frac{550672}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 16 a - 32\) , \( 44 a - 48\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(16a-32\right){x}+44a-48$ |
| 2304.1-b2 |
2304.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{7} \) |
$1.07231$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2.098868579$ |
1.211782339 |
\( \frac{73696}{3} a - \frac{624368}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -14 a - 17\) , \( 59 a + 21\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-14a-17\right){x}+59a+21$ |
| 2304.1-b3 |
2304.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{22} \) |
$1.07231$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.524717144$ |
1.211782339 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a - 47\) , \( -1033 a + 540\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a-47\right){x}-1033a+540$ |
| 2304.1-b4 |
2304.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \) |
$1.07231$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$4.197737158$ |
1.211782339 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a - 2\) , \( 2 a\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a-2\right){x}+2a$ |
| 2304.1-b5 |
2304.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{10} \) |
$1.07231$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$2.098868579$ |
1.211782339 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 13\) , \( 11 a - 12\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+13\right){x}+11a-12$ |
| 2304.1-b6 |
2304.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{14} \) |
$1.07231$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.049434289$ |
1.211782339 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 73\) , \( -289 a + 108\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+73\right){x}-289a+108$ |
| 2304.1-b7 |
2304.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{8} \) |
$1.07231$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.049434289$ |
1.211782339 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 193\) , \( 1127 a - 660\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+193\right){x}+1127a-660$ |
| 2304.1-b8 |
2304.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{10} \) |
$1.07231$ |
$(-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.524717144$ |
1.211782339 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 1153\) , \( -17785 a + 8316\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+1153\right){x}-17785a+8316$ |
*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.
