| 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-a1 |
196.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{61}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{36} \cdot 7^{2} \) |
$2.61136$ |
$(2), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.436190660$ |
0.251318210 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-171{x}-874$ |
| 196.1-a2 |
196.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{61}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{2} \) |
$2.61136$ |
$(2), (7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$35.33144352$ |
0.251318210 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}$ |
| 196.1-a3 |
196.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{61}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$2.61136$ |
$(2), (7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$3.925715946$ |
0.251318210 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+4{x}-6$ |
| 196.1-a4 |
196.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{61}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{12} \) |
$2.61136$ |
$(2), (7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$3.925715946$ |
0.251318210 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-36{x}-70$ |
| 196.1-a5 |
196.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{61}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 7^{4} \) |
$2.61136$ |
$(2), (7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$35.33144352$ |
0.251318210 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-11{x}+12$ |
| 196.1-a6 |
196.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{61}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{4} \) |
$2.61136$ |
$(2), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$0.436190660$ |
0.251318210 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2731{x}-55146$ |
| 196.1-b1 |
196.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{61}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{20} \cdot 7^{10} \) |
$2.61136$ |
$(2), (7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$1.514342134$ |
0.387783284 |
\( \frac{1298239519429}{17210368} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 44320 a - 195215\) , \( 9956241 a - 43858464\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(44320a-195215\right){x}+9956241a-43858464$ |
| 196.1-b2 |
196.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{61}) \) |
$2$ |
$[2, 0]$ |
196.1 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{2} \) |
$2.61136$ |
$(2), (7)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$37.85855336$ |
0.387783284 |
\( \frac{1221611509}{28} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -4345 a - 14790\) , \( 308643 a + 1050972\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4345a-14790\right){x}+308643a+1050972$ |
*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.
