| 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-b8 |
288.2-b |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
288.2 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{17} \cdot 3^{2} \) |
$0.97395$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$1.062735022$ |
1.606704330 |
\( \frac{145011769343}{48} a + \frac{19365113857}{16} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 224 a - 320\) , \( 1942 a - 1328\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(224a-320\right){x}+1942a-1328$ |
| 288.5-b8 |
288.5-b |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
288.5 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{17} \cdot 3^{2} \) |
$0.97395$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$1.062735022$ |
1.606704330 |
\( \frac{145011769343}{48} a + \frac{19365113857}{16} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -258 a + 255\) , \( 589 a - 2623\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-258a+255\right){x}+589a-2623$ |
| 1152.2-a8 |
1152.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1152.2 |
\( 2^{7} \cdot 3^{2} \) |
\( 2^{23} \cdot 3^{2} \) |
$1.37737$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$0.751467140$ |
1.136111527 |
\( \frac{145011769343}{48} a + \frac{19365113857}{16} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -544 a + 192\) , \( 4498 a - 6540\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-544a+192\right){x}+4498a-6540$ |
| 1152.7-a8 |
1152.7-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1152.7 |
\( 2^{7} \cdot 3^{2} \) |
\( 2^{23} \cdot 3^{2} \) |
$1.37737$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.751467140$ |
1.136111527 |
\( \frac{145011769343}{48} a + \frac{19365113857}{16} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 258 a - 770\) , \( 3548 a - 7972\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(258a-770\right){x}+3548a-7972$ |
| 1764.2-a8 |
1764.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1764.2 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{5} \cdot 3^{2} \cdot 7^{6} \) |
$1.53219$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.538031491$ |
$0.803352165$ |
1.306936936 |
\( \frac{145011769343}{48} a + \frac{19365113857}{16} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 223 a + 448\) , \( -3590 a + 6160\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(223a+448\right){x}-3590a+6160$ |
| 2592.2-a8 |
2592.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2592.2 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{17} \cdot 3^{14} \) |
$1.68693$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.354245007$ |
1.071136220 |
\( \frac{145011769343}{48} a + \frac{19365113857}{16} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 2017 a - 2879\) , \( -54451 a + 38737\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2017a-2879\right){x}-54451a+38737$ |
| 2592.5-a8 |
2592.5-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2592.5 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{17} \cdot 3^{14} \) |
$1.68693$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.354245007$ |
1.071136220 |
\( \frac{145011769343}{48} a + \frac{19365113857}{16} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -2304 a + 2304\) , \( -13628 a + 77752\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-2304a+2304\right){x}-13628a+77752$ |
| 4356.4-d8 |
4356.4-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4356.4 |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{5} \cdot 3^{2} \cdot 11^{6} \) |
$1.92070$ |
$(a), (-a+1), (-2a+3), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$0.416494274$ |
$0.640853330$ |
3.228261005 |
\( \frac{145011769343}{48} a + \frac{19365113857}{16} \) |
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 736 a - 577\) , \( -8283 a - 1747\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(736a-577\right){x}-8283a-1747$ |
| 4356.6-b8 |
4356.6-b |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4356.6 |
\( 2^{2} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{5} \cdot 3^{2} \cdot 11^{6} \) |
$1.92070$ |
$(a), (-a+1), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.665977099$ |
$0.640853330$ |
3.228261005 |
\( \frac{145011769343}{48} a + \frac{19365113857}{16} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -543 a + 960\) , \( 3123 a + 10482\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-543a+960\right){x}+3123a+10482$ |
| 9216.5-d8 |
9216.5-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
9216.5 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{35} \cdot 3^{2} \) |
$2.31645$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.375733570$ |
1.136111527 |
\( \frac{145011769343}{48} a + \frac{19365113857}{16} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -512 a + 3072\) , \( -41696 a + 800\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-512a+3072\right){x}-41696a+800$ |
| 9216.7-d8 |
9216.7-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
9216.7 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{35} \cdot 3^{2} \) |
$2.31645$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.375733570$ |
1.136111527 |
\( \frac{145011769343}{48} a + \frac{19365113857}{16} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 2048 a\) , \( 10924 a + 51420\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+2048a{x}+10924a+51420$ |
| 10368.2-d7 |
10368.2-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
10368.2 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{23} \cdot 3^{14} \) |
$2.38568$ |
$(a), (-a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$6.920692474$ |
$0.250489046$ |
5.241785665 |
\( \frac{145011769343}{48} a + \frac{19365113857}{16} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -4896 a + 1728\) , \( -121446 a + 176580\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4896a+1728\right){x}-121446a+176580$ |
| 10368.7-d7 |
10368.7-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
10368.7 |
\( 2^{7} \cdot 3^{4} \) |
\( 2^{23} \cdot 3^{14} \) |
$2.38568$ |
$(a), (-a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1.730173118$ |
$0.250489046$ |
5.241785665 |
\( \frac{145011769343}{48} a + \frac{19365113857}{16} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 2304 a - 6913\) , \( -102704 a + 199087\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(2304a-6913\right){x}-102704a+199087$ |
| 15876.2-i7 |
15876.2-i |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15876.2 |
\( 2^{2} \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{5} \cdot 3^{14} \cdot 7^{6} \) |
$2.65383$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$1$ |
$0.267784055$ |
6.477622992 |
\( \frac{145011769343}{48} a + \frac{19365113857}{16} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 2016 a + 4033\) , \( 92890 a - 158245\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(2016a+4033\right){x}+92890a-158245$ |
| 19044.4-c7 |
19044.4-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
19044.4 |
\( 2^{2} \cdot 3^{2} \cdot 23^{2} \) |
\( 2^{5} \cdot 3^{2} \cdot 23^{6} \) |
$2.77733$ |
$(a), (-a+1), (-2a+5), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.443191140$ |
5.360336192 |
\( \frac{145011769343}{48} a + \frac{19365113857}{16} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( 992 a - 2113\) , \( 24058 a - 30353\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(992a-2113\right){x}+24058a-30353$ |
| 19044.6-c7 |
19044.6-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
19044.6 |
\( 2^{2} \cdot 3^{2} \cdot 23^{2} \) |
\( 2^{5} \cdot 3^{2} \cdot 23^{6} \) |
$2.77733$ |
$(a), (-a+1), (2a+3), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.443191140$ |
5.360336192 |
\( \frac{145011769343}{48} a + \frac{19365113857}{16} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -1568 a + 959\) , \( 17512 a - 38665\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1568a+959\right){x}+17512a-38665$ |
| 36864.7-m7 |
36864.7-m |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36864.7 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{41} \cdot 3^{2} \) |
$3.27596$ |
$(a), (-a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$6.224804641$ |
$0.265683755$ |
5.000710286 |
\( \frac{145011769343}{48} a + \frac{19365113857}{16} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -2048 a - 4097\) , \( 86240 a + 85089\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-2048a-4097\right){x}+86240a+85089$ |
| 36864.7-t7 |
36864.7-t |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36864.7 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{41} \cdot 3^{2} \) |
$3.27596$ |
$(a), (-a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$6.224804641$ |
$0.265683755$ |
5.000710286 |
\( \frac{145011769343}{48} a + \frac{19365113857}{16} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -2048 a - 4097\) , \( -86240 a - 85089\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-2048a-4097\right){x}-86240a-85089$ |
| 39204.4-b7 |
39204.4-b |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39204.4 |
\( 2^{2} \cdot 3^{4} \cdot 11^{2} \) |
\( 2^{5} \cdot 3^{14} \cdot 11^{6} \) |
$3.32675$ |
$(a), (-a+1), (-2a+3), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$4.601110661$ |
$0.213617776$ |
5.943893680 |
\( \frac{145011769343}{48} a + \frac{19365113857}{16} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 6625 a - 5184\) , \( 218455 a + 39098\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(6625a-5184\right){x}+218455a+39098$ |
| 39204.6-d7 |
39204.6-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39204.6 |
\( 2^{2} \cdot 3^{4} \cdot 11^{2} \) |
\( 2^{5} \cdot 3^{14} \cdot 11^{6} \) |
$3.32675$ |
$(a), (-a+1), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1.150277665$ |
$0.213617776$ |
5.943893680 |
\( \frac{145011769343}{48} a + \frac{19365113857}{16} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -4898 a + 8641\) , \( -85468 a - 264585\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-4898a+8641\right){x}-85468a-264585$ |
*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.
