| 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 |
| 9.1-a1 |
9.1-a |
$2$ |
$11$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \cdot 7^{12} \) |
$1.44364$ |
$(3,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$11$ |
11B |
$1$ |
\( 1 \) |
$1$ |
$5.903777489$ |
1.265902769 |
\( 33176 a - 51069 \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -33 a + 76\) , \( -57 a + 620\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(-a+1\right){x}^2+\left(-33a+76\right){x}-57a+620$ |
| 9.1-a2 |
9.1-a |
$2$ |
$11$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
9.1 |
\( 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$1.44364$ |
$(3,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$11$ |
11B |
$1$ |
\( 1 \) |
$1$ |
$5.903777489$ |
1.265902769 |
\( -33176 a - 17893 \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -3 a + 18\) , \( 6\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(-3a+18\right){x}+6$ |
| 9.1-b1 |
9.1-b |
$2$ |
$11$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
9.1 |
\( 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$1.44364$ |
$(3,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$11$ |
11B |
$1$ |
\( 1 \) |
$1$ |
$5.903777489$ |
1.265902769 |
\( 33176 a - 51069 \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( a + 17\) , \( -a + 7\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+\left(a+17\right){x}-a+7$ |
| 9.1-b2 |
9.1-b |
$2$ |
$11$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \cdot 7^{12} \) |
$1.44364$ |
$(3,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$11$ |
11B |
$1$ |
\( 1 \) |
$1$ |
$5.903777489$ |
1.265902769 |
\( -33176 a - 17893 \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( 33 a + 43\) , \( 57 a + 563\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+a{x}^2+\left(33a+43\right){x}+57a+563$ |
| 14.1-a1 |
14.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{22} \cdot 7^{14} \) |
$1.61224$ |
$(2,a), (7,a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$2.778122801$ |
2.382768223 |
\( \frac{14558358177}{205520896} a + \frac{354649661145}{205520896} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 22 a - 294\) , \( 17 a + 922\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2+\left(22a-294\right){x}+17a+922$ |
| 14.1-b1 |
14.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{34} \cdot 7^{2} \) |
$1.61224$ |
$(2,a), (7,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \cdot 11 \) |
$0.027553596$ |
$2.778122801$ |
1.444384348 |
\( \frac{14558358177}{205520896} a + \frac{354649661145}{205520896} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( a + 27\) , \( -a - 48\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(-a+1\right){x}^2+\left(a+27\right){x}-a-48$ |
| 14.4-a1 |
14.4-a |
$1$ |
$1$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
14.4 |
\( 2 \cdot 7 \) |
\( 2^{34} \cdot 7^{2} \) |
$1.61224$ |
$(2,a+1), (7,a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \cdot 11 \) |
$0.027553596$ |
$2.778122801$ |
1.444384348 |
\( -\frac{14558358177}{205520896} a + \frac{184604009661}{102760448} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -a + 28\) , \( a - 49\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(-a+28\right){x}+a-49$ |
| 14.4-b1 |
14.4-b |
$1$ |
$1$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
14.4 |
\( 2 \cdot 7 \) |
\( 2^{22} \cdot 7^{14} \) |
$1.61224$ |
$(2,a+1), (7,a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$2.778122801$ |
2.382768223 |
\( -\frac{14558358177}{205520896} a + \frac{184604009661}{102760448} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -22 a - 272\) , \( -17 a + 939\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2+\left(-22a-272\right){x}-17a+939$ |
| 28.3-a1 |
28.3-a |
$1$ |
$1$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
28.3 |
\( 2^{2} \cdot 7 \) |
\( 2^{14} \cdot 7^{14} \) |
$1.91729$ |
$(2,a), (2,a+1), (7,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$0.089864392$ |
$3.874674888$ |
1.194574569 |
\( -\frac{33027317}{12544} a + \frac{94120423}{6272} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 46 a + 124\) , \( 68 a - 1512\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2+\left(46a+124\right){x}+68a-1512$ |
| 28.3-b1 |
28.3-b |
$1$ |
$1$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
28.3 |
\( 2^{2} \cdot 7 \) |
\( 2^{26} \cdot 7^{2} \) |
$1.91729$ |
$(2,a), (2,a+1), (7,a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{5} \cdot 3 \) |
$0.039940388$ |
$3.874674888$ |
6.371169421 |
\( -\frac{33027317}{12544} a + \frac{94120423}{6272} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -7 a + 1\) , \( 9 a + 49\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+{x}^2+\left(-7a+1\right){x}+9a+49$ |
| 28.4-a1 |
28.4-a |
$1$ |
$1$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
28.4 |
\( 2^{2} \cdot 7 \) |
\( 2^{14} \cdot 7^{14} \) |
$1.91729$ |
$(2,a), (2,a+1), (7,a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$0.089864392$ |
$3.874674888$ |
1.194574569 |
\( \frac{33027317}{12544} a + \frac{155213529}{12544} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -46 a + 170\) , \( -68 a - 1444\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2+\left(-46a+170\right){x}-68a-1444$ |
| 28.4-b1 |
28.4-b |
$1$ |
$1$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
28.4 |
\( 2^{2} \cdot 7 \) |
\( 2^{26} \cdot 7^{2} \) |
$1.91729$ |
$(2,a), (2,a+1), (7,a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{5} \cdot 3 \) |
$0.039940388$ |
$3.874674888$ |
6.371169421 |
\( \frac{33027317}{12544} a + \frac{155213529}{12544} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 7 a - 5\) , \( -16 a + 64\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(-a-1\right){x}^2+\left(7a-5\right){x}-16a+64$ |
| 32.2-a1 |
32.2-a |
$2$ |
$13$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
32.2 |
\( 2^{5} \) |
\( 2^{26} \) |
$1.98237$ |
$(2,a), (2,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$13$ |
13B |
$1$ |
\( 2 \) |
$1$ |
$3.004520729$ |
1.288473734 |
\( \frac{2882061}{8192} a - \frac{1102329}{4096} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( -3 a - 2\) , \( a + 6\bigr] \) |
${y}^2+a{x}{y}={x}^3+a{x}^2+\left(-3a-2\right){x}+a+6$ |
| 32.2-a2 |
32.2-a |
$2$ |
$13$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
32.2 |
\( 2^{5} \) |
\( 2^{26} \cdot 7^{12} \) |
$1.98237$ |
$(2,a), (2,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$13$ |
13B |
$1$ |
\( 2 \) |
$1$ |
$3.004520729$ |
1.288473734 |
\( -\frac{2882061}{8192} a + \frac{677403}{8192} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 17 a - 234\) , \( 199 a - 854\bigr] \) |
${y}^2+a{x}{y}={x}^3+a{x}^2+\left(17a-234\right){x}+199a-854$ |
| 32.2-b1 |
32.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
32.2 |
\( 2^{5} \) |
\( 2^{22} \) |
$1.98237$ |
$(2,a), (2,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$7.507534537$ |
3.219568753 |
\( \frac{1863}{4} a + \frac{2133}{2} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( -4 a - 5\) , \( 17\bigr] \) |
${y}^2+a{x}{y}={x}^3+a{x}^2+\left(-4a-5\right){x}+17$ |
| 32.2-c1 |
32.2-c |
$1$ |
$1$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
32.2 |
\( 2^{5} \) |
\( 2^{10} \cdot 7^{12} \) |
$1.98237$ |
$(2,a), (2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.493982326$ |
$7.507534537$ |
3.180820126 |
\( \frac{1863}{4} a + \frac{2133}{2} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -3 a + 69\) , \( 30 a - 123\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+\left(-3a+69\right){x}+30a-123$ |
| 32.2-d1 |
32.2-d |
$2$ |
$13$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
32.2 |
\( 2^{5} \) |
\( 2^{26} \cdot 3^{12} \) |
$1.98237$ |
$(2,a), (2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$13$ |
13B |
$1$ |
\( 2^{2} \cdot 13 \) |
$0.066712661$ |
$3.004520729$ |
4.469790659 |
\( \frac{2882061}{8192} a - \frac{1102329}{4096} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 12 a - 3\) , \( -45 a + 28\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(-a+1\right){x}^2+\left(12a-3\right){x}-45a+28$ |
| 32.2-d2 |
32.2-d |
$2$ |
$13$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
32.2 |
\( 2^{5} \) |
\( 2^{38} \) |
$1.98237$ |
$(2,a), (2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$13$ |
13B |
$1$ |
\( 2^{2} \) |
$0.867264605$ |
$3.004520729$ |
4.469790659 |
\( -\frac{2882061}{8192} a + \frac{677403}{8192} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -3 a + 44\) , \( -73\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+\left(-3a+44\right){x}-73$ |
| 32.5-a1 |
32.5-a |
$2$ |
$13$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
32.5 |
\( 2^{5} \) |
\( 2^{26} \cdot 7^{12} \) |
$1.98237$ |
$(2,a), (2,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$13$ |
13B |
$1$ |
\( 2 \) |
$1$ |
$3.004520729$ |
1.288473734 |
\( \frac{2882061}{8192} a - \frac{1102329}{4096} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -25 a - 228\) , \( -432 a - 182\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a+1\right){x}^2+\left(-25a-228\right){x}-432a-182$ |
| 32.5-a2 |
32.5-a |
$2$ |
$13$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
32.5 |
\( 2^{5} \) |
\( 2^{26} \) |
$1.98237$ |
$(2,a), (2,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$13$ |
13B |
$1$ |
\( 2 \) |
$1$ |
$3.004520729$ |
1.288473734 |
\( -\frac{2882061}{8192} a + \frac{677403}{8192} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -5 a - 16\) , \( -2 a + 40\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a+1\right){x}^2+\left(-5a-16\right){x}-2a+40$ |
| 32.5-b1 |
32.5-b |
$1$ |
$1$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
32.5 |
\( 2^{5} \) |
\( 2^{22} \) |
$1.98237$ |
$(2,a), (2,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$7.507534537$ |
3.219568753 |
\( -\frac{1863}{4} a + \frac{6129}{4} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -4 a - 20\) , \( -4 a + 28\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a+1\right){x}^2+\left(-4a-20\right){x}-4a+28$ |
| 32.5-c1 |
32.5-c |
$1$ |
$1$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
32.5 |
\( 2^{5} \) |
\( 2^{10} \cdot 7^{12} \) |
$1.98237$ |
$(2,a), (2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$0.493982326$ |
$7.507534537$ |
3.180820126 |
\( -\frac{1863}{4} a + \frac{6129}{4} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( a + 66\) , \( -31 a - 93\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(a+66\right){x}-31a-93$ |
| 32.5-d1 |
32.5-d |
$2$ |
$13$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
32.5 |
\( 2^{5} \) |
\( 2^{38} \) |
$1.98237$ |
$(2,a), (2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$13$ |
13B |
$1$ |
\( 2^{2} \) |
$0.867264605$ |
$3.004520729$ |
4.469790659 |
\( \frac{2882061}{8192} a - \frac{1102329}{4096} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( a + 41\) , \( -a - 73\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(a+41\right){x}-a-73$ |
| 32.5-d2 |
32.5-d |
$2$ |
$13$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
32.5 |
\( 2^{5} \) |
\( 2^{26} \cdot 3^{12} \) |
$1.98237$ |
$(2,a), (2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$13$ |
13B |
$1$ |
\( 2^{2} \cdot 13 \) |
$0.066712661$ |
$3.004520729$ |
4.469790659 |
\( -\frac{2882061}{8192} a + \frac{677403}{8192} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -12 a + 9\) , \( 45 a - 17\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(-12a+9\right){x}+45a-17$ |
| 44.3-a1 |
44.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
44.3 |
\( 2^{2} \cdot 11 \) |
\( 2^{4} \cdot 7^{12} \cdot 11^{2} \) |
$2.14665$ |
$(2,a), (2,a+1), (11,a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1.953815782$ |
$6.191019088$ |
1.152745957 |
\( \frac{5098695}{968} a - \frac{17768429}{968} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -7 a - 103\) , \( 44 a + 376\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(-7a-103\right){x}+44a+376$ |
| 44.3-a2 |
44.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
44.3 |
\( 2^{2} \cdot 11 \) |
\( 2^{12} \cdot 7^{12} \cdot 11^{6} \) |
$2.14665$ |
$(2,a), (2,a+1), (11,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$0.651271927$ |
$2.063673029$ |
1.152745957 |
\( \frac{84895883683}{907039232} a + \frac{1490011571339}{907039232} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 63 a + 422\) , \( 2 a + 2462\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(63a+422\right){x}+2a+2462$ |
| 44.3-b1 |
44.3-b |
$2$ |
$3$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
44.3 |
\( 2^{2} \cdot 11 \) |
\( 2^{16} \cdot 11^{2} \) |
$2.14665$ |
$(2,a), (2,a+1), (11,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$6.191019088$ |
7.964963002 |
\( \frac{5098695}{968} a - \frac{17768429}{968} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -4 a + 28\) , \( a - 11\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(-4a+28\right){x}+a-11$ |
| 44.3-b2 |
44.3-b |
$2$ |
$3$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
44.3 |
\( 2^{2} \cdot 11 \) |
\( 2^{24} \cdot 11^{6} \) |
$2.14665$ |
$(2,a), (2,a+1), (11,a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3^{4} \) |
$1$ |
$2.063673029$ |
7.964963002 |
\( \frac{84895883683}{907039232} a + \frac{1490011571339}{907039232} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -9 a - 17\) , \( -11 a + 105\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(-9a-17\right){x}-11a+105$ |
| 44.4-a1 |
44.4-a |
$2$ |
$3$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
44.4 |
\( 2^{2} \cdot 11 \) |
\( 2^{4} \cdot 7^{12} \cdot 11^{2} \) |
$2.14665$ |
$(2,a), (2,a+1), (11,a+10)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1.953815782$ |
$6.191019088$ |
1.152745957 |
\( -\frac{5098695}{968} a - \frac{575897}{44} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 7 a - 110\) , \( -44 a + 420\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(7a-110\right){x}-44a+420$ |
| 44.4-a2 |
44.4-a |
$2$ |
$3$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
44.4 |
\( 2^{2} \cdot 11 \) |
\( 2^{12} \cdot 7^{12} \cdot 11^{6} \) |
$2.14665$ |
$(2,a), (2,a+1), (11,a+10)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$0.651271927$ |
$2.063673029$ |
1.152745957 |
\( -\frac{84895883683}{907039232} a + \frac{71586702501}{41229056} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -63 a + 485\) , \( -2 a + 2464\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(-63a+485\right){x}-2a+2464$ |
| 44.4-b1 |
44.4-b |
$2$ |
$3$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
44.4 |
\( 2^{2} \cdot 11 \) |
\( 2^{16} \cdot 11^{2} \) |
$2.14665$ |
$(2,a), (2,a+1), (11,a+10)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$6.191019088$ |
7.964963002 |
\( -\frac{5098695}{968} a - \frac{575897}{44} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 2 a + 26\) , \( -2 a - 9\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-a{x}^2+\left(2a+26\right){x}-2a-9$ |
| 44.4-b2 |
44.4-b |
$2$ |
$3$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
44.4 |
\( 2^{2} \cdot 11 \) |
\( 2^{24} \cdot 11^{6} \) |
$2.14665$ |
$(2,a), (2,a+1), (11,a+10)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3^{4} \) |
$1$ |
$2.063673029$ |
7.964963002 |
\( -\frac{84895883683}{907039232} a + \frac{71586702501}{41229056} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 7 a - 24\) , \( 10 a + 95\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-a{x}^2+\left(7a-24\right){x}+10a+95$ |
| 52.3-a1 |
52.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
52.3 |
\( 2^{2} \cdot 13 \) |
\( 2^{4} \cdot 7^{12} \cdot 13 \) |
$2.23820$ |
$(2,a), (2,a+1), (13,a+5)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$9$ |
\( 1 \) |
$1$ |
$8.565303527$ |
1.836593855 |
\( \frac{51897}{104} a + \frac{13621}{52} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 7 a + 2\) , \( -12 a - 44\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(7a+2\right){x}-12a-44$ |
| 52.3-a2 |
52.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
52.3 |
\( 2^{2} \cdot 13 \) |
\( 2^{12} \cdot 7^{12} \cdot 13^{3} \) |
$2.23820$ |
$(2,a), (2,a+1), (13,a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$2.855101175$ |
1.836593855 |
\( \frac{6971811149}{1124864} a + \frac{38567058791}{562432} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -63 a - 523\) , \( -866 a - 4048\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(-63a-523\right){x}-866a-4048$ |
| 52.3-b1 |
52.3-b |
$3$ |
$9$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
52.3 |
\( 2^{2} \cdot 13 \) |
\( 2^{26} \cdot 13^{2} \) |
$2.23820$ |
$(2,a), (2,a+1), (13,a+5)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.782956414$ |
$3.736280450$ |
2.509039015 |
\( \frac{10433997}{86528} a + \frac{271180943}{43264} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -4 a\) , \( 16\bigr] \) |
${y}^2+a{x}{y}={x}^3-4a{x}+16$ |
| 52.3-b2 |
52.3-b |
$3$ |
$9$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
52.3 |
\( 2^{2} \cdot 13 \) |
\( 2^{30} \cdot 13^{6} \) |
$2.23820$ |
$(2,a), (2,a+1), (13,a+5)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$2.348869243$ |
$1.245426816$ |
2.509039015 |
\( -\frac{66885127292445}{158164877312} a + \frac{1236412136609419}{158164877312} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 36 a\) , \( -168 a - 608\bigr] \) |
${y}^2+a{x}{y}={x}^3+36a{x}-168a-608$ |
| 52.3-b3 |
52.3-b |
$3$ |
$9$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
52.3 |
\( 2^{2} \cdot 13 \) |
\( 2^{58} \cdot 13^{2} \) |
$2.23820$ |
$(2,a), (2,a+1), (13,a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$7.046607729$ |
$0.415142272$ |
2.509039015 |
\( \frac{325660677487873664435}{5946158883012608} a + \frac{3205893900109583423451}{5946158883012608} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 726 a - 580\) , \( 11322 a + 41580\bigr] \) |
${y}^2+a{x}{y}={x}^3+\left(726a-580\right){x}+11322a+41580$ |
| 52.3-c1 |
52.3-c |
$3$ |
$9$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
52.3 |
\( 2^{2} \cdot 13 \) |
\( 2^{14} \cdot 7^{12} \cdot 13^{2} \) |
$2.23820$ |
$(2,a), (2,a+1), (13,a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 5 \) |
$0.308656467$ |
$3.736280450$ |
4.945557033 |
\( \frac{10433997}{86528} a + \frac{271180943}{43264} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( 36 a + 124\) , \( 16 a - 816\bigr] \) |
${y}^2+{x}{y}={x}^3-a{x}^2+\left(36a+124\right){x}+16a-816$ |
| 52.3-c2 |
52.3-c |
$3$ |
$9$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
52.3 |
\( 2^{2} \cdot 13 \) |
\( 2^{18} \cdot 7^{12} \cdot 13^{6} \) |
$2.23820$ |
$(2,a), (2,a+1), (13,a+5)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \cdot 5 \) |
$0.925969403$ |
$1.245426816$ |
4.945557033 |
\( -\frac{66885127292445}{158164877312} a + \frac{1236412136609419}{158164877312} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -449 a - 41\) , \( 6123 a - 24085\bigr] \) |
${y}^2+{x}{y}={x}^3-a{x}^2+\left(-449a-41\right){x}+6123a-24085$ |
| 52.3-c3 |
52.3-c |
$3$ |
$9$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
52.3 |
\( 2^{2} \cdot 13 \) |
\( 2^{46} \cdot 7^{12} \cdot 13^{2} \) |
$2.23820$ |
$(2,a), (2,a+1), (13,a+5)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \cdot 5 \) |
$2.777908211$ |
$0.415142272$ |
4.945557033 |
\( \frac{325660677487873664435}{5946158883012608} a + \frac{3205893900109583423451}{5946158883012608} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -8924 a + 4254\) , \( -497362 a + 2476568\bigr] \) |
${y}^2+{x}{y}={x}^3-a{x}^2+\left(-8924a+4254\right){x}-497362a+2476568$ |
| 52.3-d1 |
52.3-d |
$2$ |
$3$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
52.3 |
\( 2^{2} \cdot 13 \) |
\( 2^{16} \cdot 13 \) |
$2.23820$ |
$(2,a), (2,a+1), (13,a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$8.565303527$ |
5.509781566 |
\( \frac{51897}{104} a + \frac{13621}{52} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -5 a + 19\) , \( 3 a + 7\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(-5a+19\right){x}+3a+7$ |
| 52.3-d2 |
52.3-d |
$2$ |
$3$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
52.3 |
\( 2^{2} \cdot 13 \) |
\( 2^{24} \cdot 13^{3} \) |
$2.23820$ |
$(2,a), (2,a+1), (13,a+5)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 3^{4} \) |
$1$ |
$2.855101175$ |
5.509781566 |
\( \frac{6971811149}{1124864} a + \frac{38567058791}{562432} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 64\) , \( 29 a - 207\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-{x}^2+64{x}+29a-207$ |
| 52.4-a1 |
52.4-a |
$2$ |
$3$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
52.4 |
\( 2^{2} \cdot 13 \) |
\( 2^{4} \cdot 7^{12} \cdot 13 \) |
$2.23820$ |
$(2,a), (2,a+1), (13,a+7)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$8.565303527$ |
1.836593855 |
\( -\frac{51897}{104} a + \frac{79139}{104} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -7 a + 9\) , \( 12 a - 56\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(-7a+9\right){x}+12a-56$ |
| 52.4-a2 |
52.4-a |
$2$ |
$3$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
52.4 |
\( 2^{2} \cdot 13 \) |
\( 2^{12} \cdot 7^{12} \cdot 13^{3} \) |
$2.23820$ |
$(2,a), (2,a+1), (13,a+7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$2.855101175$ |
1.836593855 |
\( -\frac{6971811149}{1124864} a + \frac{84105928731}{1124864} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 63 a - 586\) , \( 866 a - 4914\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+\left(63a-586\right){x}+866a-4914$ |
| 52.4-b1 |
52.4-b |
$3$ |
$9$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
52.4 |
\( 2^{2} \cdot 13 \) |
\( 2^{14} \cdot 7^{12} \cdot 13^{2} \) |
$2.23820$ |
$(2,a), (2,a+1), (13,a+7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 5 \) |
$0.308656467$ |
$3.736280450$ |
4.945557033 |
\( -\frac{10433997}{86528} a + \frac{552795883}{86528} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( -36 a + 160\) , \( -16 a - 800\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(a-1\right){x}^2+\left(-36a+160\right){x}-16a-800$ |
| 52.4-b2 |
52.4-b |
$3$ |
$9$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
52.4 |
\( 2^{2} \cdot 13 \) |
\( 2^{18} \cdot 7^{12} \cdot 13^{6} \) |
$2.23820$ |
$(2,a), (2,a+1), (13,a+7)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \cdot 5 \) |
$0.925969403$ |
$1.245426816$ |
4.945557033 |
\( \frac{66885127292445}{158164877312} a + \frac{584763504658487}{79082438656} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 449 a - 490\) , \( -6123 a - 17962\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(a-1\right){x}^2+\left(449a-490\right){x}-6123a-17962$ |
| 52.4-b3 |
52.4-b |
$3$ |
$9$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
52.4 |
\( 2^{2} \cdot 13 \) |
\( 2^{46} \cdot 7^{12} \cdot 13^{2} \) |
$2.23820$ |
$(2,a), (2,a+1), (13,a+7)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \cdot 5 \) |
$2.777908211$ |
$0.415142272$ |
4.945557033 |
\( -\frac{325660677487873664435}{5946158883012608} a + \frac{1765777288798728543943}{2973079441506304} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 8924 a - 4670\) , \( 497362 a + 1979206\bigr] \) |
${y}^2+{x}{y}={x}^3+\left(a-1\right){x}^2+\left(8924a-4670\right){x}+497362a+1979206$ |
| 52.4-c1 |
52.4-c |
$3$ |
$9$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
52.4 |
\( 2^{2} \cdot 13 \) |
\( 2^{26} \cdot 13^{2} \) |
$2.23820$ |
$(2,a), (2,a+1), (13,a+7)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.782956414$ |
$3.736280450$ |
2.509039015 |
\( -\frac{10433997}{86528} a + \frac{552795883}{86528} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 4 a - 4\) , \( 16\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3-a{x}^2+\left(4a-4\right){x}+16$ |
| 52.4-c2 |
52.4-c |
$3$ |
$9$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
52.4 |
\( 2^{2} \cdot 13 \) |
\( 2^{30} \cdot 13^{6} \) |
$2.23820$ |
$(2,a), (2,a+1), (13,a+7)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$2.348869243$ |
$1.245426816$ |
2.509039015 |
\( \frac{66885127292445}{158164877312} a + \frac{584763504658487}{79082438656} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -36 a + 36\) , \( 168 a - 776\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3-a{x}^2+\left(-36a+36\right){x}+168a-776$ |
| 52.4-c3 |
52.4-c |
$3$ |
$9$ |
\(\Q(\sqrt{-87}) \) |
$2$ |
$[0, 1]$ |
52.4 |
\( 2^{2} \cdot 13 \) |
\( 2^{58} \cdot 13^{2} \) |
$2.23820$ |
$(2,a), (2,a+1), (13,a+7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$7.046607729$ |
$0.415142272$ |
2.509039015 |
\( -\frac{325660677487873664435}{5946158883012608} a + \frac{1765777288798728543943}{2973079441506304} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -726 a + 146\) , \( -11322 a + 52902\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^3-a{x}^2+\left(-726a+146\right){x}-11322a+52902$ |
*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.
