| 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 |
| 121.1-a1 |
121.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{22}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$2.78020$ |
$(7a-33)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$0.263658012$ |
$24.82216951$ |
1.395305708 |
\( -204288 a - 958144 \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -390 a + 1826\) , \( 50910 a - 238791\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-390a+1826\right){x}+50910a-238791$ |
| 121.1-a2 |
121.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{22}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$2.78020$ |
$(7a-33)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$0.790974037$ |
$8.274056503$ |
1.395305708 |
\( 204288 a - 958144 \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 4 a - 22\) , \( 19 a - 91\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(4a-22\right){x}+19a-91$ |
| 121.1-b1 |
121.1-b |
$2$ |
$11$ |
\(\Q(\sqrt{22}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{4} \) |
$2.78020$ |
$(7a-33)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$11$ |
11B.1.6 |
|
\( 1 \) |
$1$ |
$1.039981560$ |
5.887227655 |
\( -24729001 \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -30\) , \( -76\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-30{x}-76$ |
| 121.1-b2 |
121.1-b |
$2$ |
$11$ |
\(\Q(\sqrt{22}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{8} \) |
$2.78020$ |
$(7a-33)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$11$ |
11B.1.4 |
|
\( 1 \) |
$1$ |
$11.43979716$ |
5.887227655 |
\( -121 \) |
\( \bigl[a + 1\) , \( a\) , \( a\) , \( 41720 a - 195643\) , \( -39280465 a + 184241784\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(41720a-195643\right){x}-39280465a+184241784$ |
| 121.1-c1 |
121.1-c |
$2$ |
$11$ |
\(\Q(\sqrt{22}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{4} \) |
$2.78020$ |
$(7a-33)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$11$ |
11B.1.5 |
$1$ |
\( 1 \) |
$1.338921711$ |
$30.53686771$ |
8.717025796 |
\( -24729001 \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( 496790 a - 2330100\) , \( -413009700 a + 1937187283\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(496790a-2330100\right){x}-413009700a+1937187283$ |
| 121.1-c2 |
121.1-c |
$2$ |
$11$ |
\(\Q(\sqrt{22}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{8} \) |
$2.78020$ |
$(7a-33)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$11$ |
11B.1.7 |
$1$ |
\( 1 \) |
$14.72813882$ |
$2.776078883$ |
8.717025796 |
\( -121 \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -2\) , \( -7\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-2{x}-7$ |
| 121.1-d1 |
121.1-d |
$2$ |
$11$ |
\(\Q(\sqrt{22}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{6} \) |
$2.78020$ |
$(7a-33)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$11$ |
11B.1.3 |
$1$ |
\( 2^{2} \) |
$0.089785156$ |
$23.06325055$ |
1.765930918 |
\( -32768 \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -7\) , \( 10\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-7{x}+10$ |
| 121.1-d2 |
121.1-d |
$2$ |
$11$ |
\(\Q(\sqrt{22}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{6} \) |
$2.78020$ |
$(7a-33)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-11$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$11$ |
11B.1.8 |
$1$ |
\( 2^{2} \) |
$0.987636717$ |
$2.096659141$ |
1.765930918 |
\( -32768 \) |
\( \bigl[0\) , \( -1\) , \( a + 1\) , \( 121352 a - 569191\) , \( 51092233 a - 239643823\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(121352a-569191\right){x}+51092233a-239643823$ |
| 121.1-e1 |
121.1-e |
$2$ |
$3$ |
\(\Q(\sqrt{22}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$2.78020$ |
$(7a-33)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$0.790974037$ |
$8.274056503$ |
1.395305708 |
\( -204288 a - 958144 \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -5 a - 22\) , \( -20 a - 91\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-5a-22\right){x}-20a-91$ |
| 121.1-e2 |
121.1-e |
$2$ |
$3$ |
\(\Q(\sqrt{22}) \) |
$2$ |
$[2, 0]$ |
121.1 |
\( 11^{2} \) |
\( 11^{2} \) |
$2.78020$ |
$(7a-33)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$0.263658012$ |
$24.82216951$ |
1.395305708 |
\( 204288 a - 958144 \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 389 a + 1826\) , \( -50911 a - 238791\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(389a+1826\right){x}-50911a-238791$ |
*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.
