| 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 |
| 161.1-a2 |
161.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
161.1 |
\( 7 \cdot 23 \) |
\( 7 \cdot 23^{9} \) |
$0.84216$ |
$(-2a+1), (-2a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$0.963842486$ |
0.728596434 |
\( \frac{72000442968309760}{12608068630241} a + \frac{219811714610757632}{12608068630241} \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -59 a + 69\) , \( -2 a + 254\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-59a+69\right){x}-2a+254$ |
| 10304.1-c2 |
10304.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
10304.1 |
\( 2^{6} \cdot 7 \cdot 23 \) |
\( 2^{6} \cdot 7 \cdot 23^{9} \) |
$2.38199$ |
$(a), (-2a+1), (-2a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 1 \) |
$2.975847160$ |
$0.681539557$ |
3.066286011 |
\( \frac{72000442968309760}{12608068630241} a + \frac{219811714610757632}{12608068630241} \) |
\( \bigl[0\) , \( -a + 1\) , \( a\) , \( 129 a - 19\) , \( 267 a + 752\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(129a-19\right){x}+267a+752$ |
| 10304.13-c2 |
10304.13-c |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
10304.13 |
\( 2^{6} \cdot 7 \cdot 23 \) |
\( 2^{6} \cdot 7 \cdot 23^{9} \) |
$2.38199$ |
$(-a+1), (-2a+1), (-2a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 1 \) |
$2.092982546$ |
$0.681539557$ |
2.156590293 |
\( \frac{72000442968309760}{12608068630241} a + \frac{219811714610757632}{12608068630241} \) |
\( \bigl[0\) , \( -a\) , \( a + 1\) , \( 51 a - 190\) , \( -309 a + 948\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(51a-190\right){x}-309a+948$ |
| 13041.1-b2 |
13041.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
13041.1 |
\( 3^{4} \cdot 7 \cdot 23 \) |
\( 3^{12} \cdot 7 \cdot 23^{9} \) |
$2.52648$ |
$(-2a+1), (-2a+5), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$2.521122252$ |
$0.321280828$ |
2.449174245 |
\( \frac{72000442968309760}{12608068630241} a + \frac{219811714610757632}{12608068630241} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -540 a + 624\) , \( 505 a - 8562\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-540a+624\right){x}+505a-8562$ |
| 18032.1-d2 |
18032.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
18032.1 |
\( 2^{4} \cdot 7^{2} \cdot 23 \) |
\( 2^{12} \cdot 7^{7} \cdot 23^{9} \) |
$2.73967$ |
$(a), (-2a+1), (-2a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$2.892126344$ |
$0.182149108$ |
3.185776281 |
\( \frac{72000442968309760}{12608068630241} a + \frac{219811714610757632}{12608068630241} \) |
\( \bigl[0\) , \( -a - 1\) , \( a\) , \( 1037 a + 1549\) , \( -22887 a + 46652\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(1037a+1549\right){x}-22887a+46652$ |
| 18032.9-b2 |
18032.9-b |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
18032.9 |
\( 2^{4} \cdot 7^{2} \cdot 23 \) |
\( 2^{12} \cdot 7^{7} \cdot 23^{9} \) |
$2.73967$ |
$(-a+1), (-2a+1), (-2a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.182149108$ |
2.478452106 |
\( \frac{72000442968309760}{12608068630241} a + \frac{219811714610757632}{12608068630241} \) |
\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( -615 a - 2035\) , \( 18185 a + 31481\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-615a-2035\right){x}+18185a+31481$ |
| 25921.1-a2 |
25921.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
25921.1 |
\( 7^{2} \cdot 23^{2} \) |
\( 7^{7} \cdot 23^{15} \) |
$2.99986$ |
$(-2a+1), (-2a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{3} \) |
$1.649708422$ |
$0.075961429$ |
1.515658215 |
\( \frac{72000442968309760}{12608068630241} a + \frac{219811714610757632}{12608068630241} \) |
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 8185 a + 5189\) , \( -122016 a + 663791\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(8185a+5189\right){x}-122016a+663791$ |
| 41216.9-f2 |
41216.9-f |
$3$ |
$9$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
41216.9 |
\( 2^{8} \cdot 7 \cdot 23 \) |
\( 2^{24} \cdot 7 \cdot 23^{9} \) |
$3.36864$ |
$(a), (-a+1), (-2a+1), (-2a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 3^{2} \) |
$1$ |
$0.240960621$ |
1.639341977 |
\( \frac{72000442968309760}{12608068630241} a + \frac{219811714610757632}{12608068630241} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -959 a + 1109\) , \( 927 a - 19285\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-959a+1109\right){x}+927a-19285$ |
*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.
