| 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 |
| 288.2-b6 |
288.2-b |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
288.2 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{4} \) |
$0.97395$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.125470044$ |
1.606704330 |
\( \frac{56620795}{2304} a + \frac{115022599}{2304} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 14 a - 20\) , \( 28 a - 20\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(14a-20\right){x}+28a-20$ |
| 288.5-b6 |
288.5-b |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
288.5 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{4} \) |
$0.97395$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$2.125470044$ |
1.606704330 |
\( \frac{56620795}{2304} a + \frac{115022599}{2304} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -18 a + 15\) , \( 13 a - 31\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-18a+15\right){x}+13a-31$ |
| 1152.2-a6 |
1152.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1152.2 |
\( 2^{7} \cdot 3^{2} \) |
\( 2^{28} \cdot 3^{4} \) |
$1.37737$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.502934281$ |
1.136111527 |
\( \frac{56620795}{2304} a + \frac{115022599}{2304} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -34 a + 12\) , \( 64 a - 96\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-34a+12\right){x}+64a-96$ |
| 1152.7-a6 |
1152.7-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1152.7 |
\( 2^{7} \cdot 3^{2} \) |
\( 2^{28} \cdot 3^{4} \) |
$1.37737$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.502934281$ |
1.136111527 |
\( \frac{56620795}{2304} a + \frac{115022599}{2304} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 18 a - 50\) , \( 44 a - 148\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(18a-50\right){x}+44a-148$ |
| 1764.2-a6 |
1764.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1764.2 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{10} \cdot 3^{4} \cdot 7^{6} \) |
$1.53219$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.269015745$ |
$1.606704330$ |
1.306936936 |
\( \frac{56620795}{2304} a + \frac{115022599}{2304} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 13 a + 28\) , \( -62 a + 112\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(13a+28\right){x}-62a+112$ |
| 2592.2-a6 |
2592.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2592.2 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{22} \cdot 3^{16} \) |
$1.68693$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.708490014$ |
1.071136220 |
\( \frac{56620795}{2304} a + \frac{115022599}{2304} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 127 a - 179\) , \( -883 a + 721\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(127a-179\right){x}-883a+721$ |
| 2592.5-a6 |
2592.5-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2592.5 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{22} \cdot 3^{16} \) |
$1.68693$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.708490014$ |
1.071136220 |
\( \frac{56620795}{2304} a + \frac{115022599}{2304} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -144 a + 144\) , \( -236 a + 1288\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-144a+144\right){x}-236a+1288$ |
| 4356.4-d6 |
4356.4-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4356.4 |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{10} \cdot 3^{4} \cdot 11^{6} \) |
$1.92070$ |
$(a), (-a+1), (-2a+3), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$0.208247137$ |
$1.281706661$ |
3.228261005 |
\( \frac{56620795}{2304} a + \frac{115022599}{2304} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 46 a - 37\) , \( -135 a - 43\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(46a-37\right){x}-135a-43$ |
| 4356.6-b6 |
4356.6-b |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4356.6 |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{10} \cdot 3^{4} \cdot 11^{6} \) |
$1.92070$ |
$(a), (-a+1), (2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.832988549$ |
$1.281706661$ |
3.228261005 |
\( \frac{56620795}{2304} a + \frac{115022599}{2304} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -33 a + 60\) , \( 45 a + 198\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-33a+60\right){x}+45a+198$ |
| 9216.5-d6 |
9216.5-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
9216.5 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{40} \cdot 3^{4} \) |
$2.31645$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.751467140$ |
1.136111527 |
\( \frac{56620795}{2304} a + \frac{115022599}{2304} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -32 a + 192\) , \( -608 a + 32\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-32a+192\right){x}-608a+32$ |
| 9216.7-d6 |
9216.7-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
9216.7 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{40} \cdot 3^{4} \) |
$2.31645$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.751467140$ |
1.136111527 |
\( \frac{56620795}{2304} a + \frac{115022599}{2304} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 128 a\) , \( 172 a + 732\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+128a{x}+172a+732$ |
| 10368.2-d5 |
10368.2-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
10368.2 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{28} \cdot 3^{16} \) |
$2.38568$ |
$(a), (-a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$3.460346237$ |
$0.500978093$ |
5.241785665 |
\( \frac{56620795}{2304} a + \frac{115022599}{2304} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -306 a + 108\) , \( -1728 a + 2592\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-306a+108\right){x}-1728a+2592$ |
| 10368.7-d5 |
10368.7-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
10368.7 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{28} \cdot 3^{16} \) |
$2.38568$ |
$(a), (-a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$0.865086559$ |
$0.500978093$ |
5.241785665 |
\( \frac{56620795}{2304} a + \frac{115022599}{2304} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 144 a - 433\) , \( -1616 a + 2959\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(144a-433\right){x}-1616a+2959$ |
| 15876.2-i5 |
15876.2-i |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15876.2 |
\( 2^{2} \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{10} \cdot 3^{16} \cdot 7^{6} \) |
$2.65383$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$1$ |
$0.535568110$ |
6.477622992 |
\( \frac{56620795}{2304} a + \frac{115022599}{2304} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 126 a + 253\) , \( 1414 a - 2509\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(126a+253\right){x}+1414a-2509$ |
| 19044.4-c5 |
19044.4-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
19044.4 |
\( 2^{2} \cdot 3^{2} \cdot 23^{2} \) |
\( 2^{10} \cdot 3^{4} \cdot 23^{6} \) |
$2.77733$ |
$(a), (-a+1), (-2a+5), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.886382281$ |
5.360336192 |
\( \frac{56620795}{2304} a + \frac{115022599}{2304} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( 62 a - 133\) , \( 394 a - 449\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(62a-133\right){x}+394a-449$ |
| 19044.6-c5 |
19044.6-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
19044.6 |
\( 2^{2} \cdot 3^{2} \cdot 23^{2} \) |
\( 2^{10} \cdot 3^{4} \cdot 23^{6} \) |
$2.77733$ |
$(a), (-a+1), (2a+3), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.886382281$ |
5.360336192 |
\( \frac{56620795}{2304} a + \frac{115022599}{2304} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -98 a + 59\) , \( 298 a - 661\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-98a+59\right){x}+298a-661$ |
| 36864.7-m5 |
36864.7-m |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36864.7 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{46} \cdot 3^{4} \) |
$3.27596$ |
$(a), (-a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$3.112402320$ |
$0.531367511$ |
5.000710286 |
\( \frac{56620795}{2304} a + \frac{115022599}{2304} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -128 a - 257\) , \( 1376 a + 1377\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-128a-257\right){x}+1376a+1377$ |
| 36864.7-t5 |
36864.7-t |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36864.7 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{46} \cdot 3^{4} \) |
$3.27596$ |
$(a), (-a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$3.112402320$ |
$0.531367511$ |
5.000710286 |
\( \frac{56620795}{2304} a + \frac{115022599}{2304} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -128 a - 257\) , \( -1376 a - 1377\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-128a-257\right){x}-1376a-1377$ |
| 39204.4-b5 |
39204.4-b |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39204.4 |
\( 2^{2} \cdot 3^{4} \cdot 11^{2} \) |
\( 2^{10} \cdot 3^{16} \cdot 11^{6} \) |
$3.32675$ |
$(a), (-a+1), (-2a+3), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$2.300555330$ |
$0.427235553$ |
5.943893680 |
\( \frac{56620795}{2304} a + \frac{115022599}{2304} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 415 a - 324\) , \( 3319 a + 650\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(415a-324\right){x}+3319a+650$ |
| 39204.6-d5 |
39204.6-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39204.6 |
\( 2^{2} \cdot 3^{4} \cdot 11^{2} \) |
\( 2^{10} \cdot 3^{16} \cdot 11^{6} \) |
$3.32675$ |
$(a), (-a+1), (2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$0.575138832$ |
$0.427235553$ |
5.943893680 |
\( \frac{56620795}{2304} a + \frac{115022599}{2304} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -308 a + 541\) , \( -1282 a - 4197\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-308a+541\right){x}-1282a-4197$ |
*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.
