| 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 |
| 196.1-b3 |
196.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-51}) \) |
$2$ |
$[0, 1]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{12} \cdot 7^{6} \) |
$2.38774$ |
$(2), (7)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$7.403962476$ |
$2.626251405$ |
5.445595949 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 40\) , \( 155\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2+40{x}+155$ |
| 98.2-b3 |
98.2-b |
$6$ |
$18$ |
\(\Q(\sqrt{-17}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$2.31846$ |
$(2,a+1), (7,a+2), (7,a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2 \) |
$7.403962476$ |
$2.626251405$ |
4.716024430 |
\( \frac{9938375}{21952} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 8\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^3+{x}^2+8{x}$ |
| 28.2-a3 |
28.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-119}) \) |
$2$ |
$[0, 1]$ |
28.2 |
\( 2^{2} \cdot 7 \) |
\( 2^{12} \cdot 7^{18} \) |
$2.24234$ |
$(2,a), (2,a+1), (7,a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{3} \) |
$1.850990619$ |
$2.626251405$ |
3.564979377 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 220\) , \( 2192\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2+220{x}+2192$ |
| 98.2-a3 |
98.2-a |
$6$ |
$18$ |
\(\Q(\sqrt{-34}) \) |
$2$ |
$[0, 1]$ |
98.2 |
\( 2 \cdot 7^{2} \) |
\( 2^{24} \cdot 7^{6} \) |
$3.27880$ |
$(2,a), (7,a+1), (7,a+6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2 \) |
$7.403962476$ |
$2.626251405$ |
3.334732855 |
\( \frac{9938375}{21952} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 65\) , \( -31\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+65{x}-31$ |
| 98.1-c3 |
98.1-c |
$6$ |
$18$ |
\(\Q(\sqrt{-85}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{12} \cdot 5^{12} \cdot 7^{6} \) |
$5.18423$ |
$(2,a+1), (7)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2 \cdot 3 \) |
$5.070582013$ |
$2.626251405$ |
8.666343463 |
\( \frac{9938375}{21952} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 277\) , \( -473\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2+277{x}-473$ |
| 98.1-b3 |
98.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-102}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \cdot 17^{12} \) |
$5.67904$ |
$(2,a), (7)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2 \cdot 3 \) |
$8.598615992$ |
$2.626251405$ |
13.41578273 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 1295\) , \( -29547\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2+1295{x}-29547$ |
| 28.1-a3 |
28.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-595}) \) |
$2$ |
$[0, 1]$ |
28.1 |
\( 2^{2} \cdot 7 \) |
\( 2^{12} \cdot 7^{6} \cdot 13^{12} \) |
$5.01403$ |
$(7,a+3), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$4.630558560$ |
$5.252502811$ |
11.96526819 |
\( \frac{9938375}{21952} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( -47 a - 96\) , \( 1028 a - 6488\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^3+\left(-47a-96\right){x}+1028a-6488$ |
| 98.1-b3 |
98.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-170}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \cdot 17^{12} \) |
$7.33161$ |
$(2,a), (7)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2 \cdot 3 \) |
$18.80212787$ |
$5.252502811$ |
22.72323132 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 1295\) , \( -29547\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2+1295{x}-29547$ |
| 98.1-d3 |
98.1-d |
$6$ |
$18$ |
\(\Q(\sqrt{-221}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \cdot 13^{12} \) |
$8.35932$ |
$(2,a+1), (7)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2 \cdot 3 \) |
$25.68064810$ |
$5.252502811$ |
27.22058104 |
\( \frac{9938375}{21952} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 1738\) , \( -6148\bigr] \) |
${y}^2+a{x}{y}={x}^3+{x}^2+1738{x}-6148$ |
| 14.1-a3 |
14.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-238}) \) |
$2$ |
$[0, 1]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{12} \cdot 7^{6} \cdot 17^{12} \) |
$5.33321$ |
$(2,a), (7,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \) |
$7.403962476$ |
$5.252502811$ |
2.520821092 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 1295\) , \( -29547\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2+1295{x}-29547$ |
| 14.1-c3 |
14.1-c |
$6$ |
$18$ |
\(\Q(\sqrt{-357}) \) |
$2$ |
$[0, 1]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{12} \cdot 7^{6} \cdot 17^{12} \) |
$6.53183$ |
$(2,a+1), (7,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$4$ |
\( 2^{2} \) |
$7.403962476$ |
$5.252502811$ |
8.232967213 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 1295\) , \( -29547\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2+1295{x}-29547$ |
| 196.1-b3 |
196.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$1.37856$ |
$(-a+2), (-a-1), (7)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1.850990619$ |
$3.925715946$ |
1.174917493 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+4{x}-6$ |
*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.
