| 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 |
| 86.4-a3 |
86.4-a |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
86.4 |
\( 2 \cdot 43 \) |
\( 2^{5} \cdot 43 \) |
$0.71997$ |
$(-a+1), (2a+5)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$6.444345720$ |
0.541274163 |
\( -\frac{5858999}{1376} a + \frac{18653653}{688} \) |
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( -a - 1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-a-1\right){x}$ |
| 2752.14-b3 |
2752.14-b |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2752.14 |
\( 2^{6} \cdot 43 \) |
\( 2^{23} \cdot 43 \) |
$1.71238$ |
$(-a+1), (2a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.160537094$ |
$2.278420279$ |
2.211974923 |
\( -\frac{5858999}{1376} a + \frac{18653653}{688} \) |
\( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( -3 a - 15\) , \( 10 a + 14\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a-15\right){x}+10a+14$ |
| 5504.4-g3 |
5504.4-g |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
5504.4 |
\( 2^{7} \cdot 43 \) |
\( 2^{11} \cdot 43 \) |
$2.03637$ |
$(a), (-a+1), (2a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 5 \) |
$0.134535550$ |
$4.556840559$ |
4.634275720 |
\( -\frac{5858999}{1376} a + \frac{18653653}{688} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( a + 3\) , \( 3 a - 4\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(a+3\right){x}+3a-4$ |
| 6966.4-a3 |
6966.4-a |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
6966.4 |
\( 2 \cdot 3^{4} \cdot 43 \) |
\( 2^{5} \cdot 3^{12} \cdot 43 \) |
$2.15990$ |
$(-a+1), (2a+5), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 5 \) |
$0.119712470$ |
$2.148115240$ |
3.887836029 |
\( -\frac{5858999}{1376} a + \frac{18653653}{688} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -13 a + 1\) , \( -13 a + 11\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-13a+1\right){x}-13a+11$ |
| 11008.10-b3 |
11008.10-b |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
11008.10 |
\( 2^{8} \cdot 43 \) |
\( 2^{29} \cdot 43 \) |
$2.42167$ |
$(a), (-a+1), (2a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.420131775$ |
$1.611086430$ |
4.093316556 |
\( -\frac{5858999}{1376} a + \frac{18653653}{688} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -22 a - 1\) , \( -67 a + 55\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-22a-1\right){x}-67a+55$ |
| 29584.15-a3 |
29584.15-a |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
29584.15 |
\( 2^{4} \cdot 43^{2} \) |
\( 2^{17} \cdot 43^{7} \) |
$3.10064$ |
$(-a+1), (2a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{3} \) |
$0.742153218$ |
$0.491376754$ |
4.410716468 |
\( -\frac{5858999}{1376} a + \frac{18653653}{688} \) |
\( \bigl[0\) , \( a + 1\) , \( a + 1\) , \( 86 a + 291\) , \( 1803 a - 1919\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(86a+291\right){x}+1803a-1919$ |
| 33712.10-c3 |
33712.10-c |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
33712.10 |
\( 2^{4} \cdot 7^{2} \cdot 43 \) |
\( 2^{17} \cdot 7^{6} \cdot 43 \) |
$3.20357$ |
$(-a+1), (-2a+1), (2a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$1.217866867$ |
1.841241634 |
\( -\frac{5858999}{1376} a + \frac{18653653}{688} \) |
\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( 22 a - 61\) , \( 90 a - 124\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(22a-61\right){x}+90a-124$ |
| 44032.10-f3 |
44032.10-f |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
44032.10 |
\( 2^{10} \cdot 43 \) |
\( 2^{23} \cdot 43 \) |
$3.42476$ |
$(a), (-a+1), (2a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.616036781$ |
$2.278420279$ |
4.244059340 |
\( -\frac{5858999}{1376} a + \frac{18653653}{688} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 12 a - 12\) , \( -18 a + 10\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(12a-12\right){x}-18a+10$ |
| 44032.14-d3 |
44032.14-d |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
44032.14 |
\( 2^{10} \cdot 43 \) |
\( 2^{35} \cdot 43 \) |
$3.42476$ |
$(a), (-a+1), (2a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$1.139210139$ |
1.722323840 |
\( -\frac{5858999}{1376} a + \frac{18653653}{688} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 47 a - 46\) , \( -143 a - 14\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(47a-46\right){x}-143a-14$ |
*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.
