| 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 |
| 242.3-a4 |
242.3-a |
$4$ |
$33$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
242.3 |
\( 2 \cdot 11^{2} \) |
\( 2^{3} \cdot 11^{8} \) |
$0.93248$ |
$(a), (2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 11$ |
3B.1.2, 11B.3.1 |
$1$ |
\( 1 \) |
$1$ |
$0.883843034$ |
0.668122533 |
\( -\frac{424896929}{8} a + \frac{1123216443}{8} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -96 a - 300\) , \( 831 a + 2090\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-96a-300\right){x}+831a+2090$ |
| 1936.3-b4 |
1936.3-b |
$4$ |
$33$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1936.3 |
\( 2^{4} \cdot 11^{2} \) |
\( 2^{15} \cdot 11^{2} \) |
$1.56825$ |
$(a), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 11$ |
3B, 11B |
$1$ |
\( 2^{2} \) |
$0.226495270$ |
$1.465687859$ |
2.007574132 |
\( -\frac{424896929}{8} a + \frac{1123216443}{8} \) |
\( \bigl[0\) , \( -a\) , \( a\) , \( 20 a + 121\) , \( 385 a - 375\bigr] \) |
${y}^2+a{y}={x}^{3}-a{x}^{2}+\left(20a+121\right){x}+385a-375$ |
| 3872.15-d4 |
3872.15-d |
$4$ |
$33$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.15 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{15} \cdot 11^{2} \) |
$1.86497$ |
$(a), (-a+1), (2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 11$ |
3B, 11B |
$1$ |
\( 3 \) |
$1$ |
$1.465687859$ |
3.323867636 |
\( -\frac{424896929}{8} a + \frac{1123216443}{8} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 4 a - 136\) , \( 49 a - 647\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(4a-136\right){x}+49a-647$ |
| 7744.3-a4 |
7744.3-a |
$4$ |
$33$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7744.3 |
\( 2^{6} \cdot 11^{2} \) |
\( 2^{21} \cdot 11^{8} \) |
$2.21783$ |
$(a), (2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 11$ |
3B, 11B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$0.312485701$ |
1.417301922 |
\( -\frac{424896929}{8} a + \frac{1123216443}{8} \) |
\( \bigl[0\) , \( a\) , \( a\) , \( -2159 a + 346\) , \( 42156 a - 44433\bigr] \) |
${y}^2+a{y}={x}^{3}+a{x}^{2}+\left(-2159a+346\right){x}+42156a-44433$ |
| 7744.3-b4 |
7744.3-b |
$4$ |
$33$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7744.3 |
\( 2^{6} \cdot 11^{2} \) |
\( 2^{21} \cdot 11^{2} \) |
$2.21783$ |
$(a), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 11$ |
3B, 11B |
$1$ |
\( 2^{2} \) |
$0.456611854$ |
$1.036397824$ |
2.861835308 |
\( -\frac{424896929}{8} a + \frac{1123216443}{8} \) |
\( \bigl[0\) , \( a + 1\) , \( a\) , \( 103 a - 283\) , \( 882 a - 1804\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(103a-283\right){x}+882a-1804$ |
| 11858.3-a4 |
11858.3-a |
$4$ |
$33$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
11858.3 |
\( 2 \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{3} \cdot 7^{6} \cdot 11^{2} \) |
$2.46712$ |
$(a), (-2a+1), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 11$ |
3B, 11B |
$1$ |
\( 2 \) |
$0.755687649$ |
$1.107955878$ |
2.531662201 |
\( -\frac{424896929}{8} a + \frac{1123216443}{8} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -176 a + 104\) , \( -744 a + 1636\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-176a+104\right){x}-744a+1636$ |
| 15488.21-a4 |
15488.21-a |
$4$ |
$33$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.21 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{9} \cdot 11^{2} \) |
$2.63746$ |
$(a), (-a+1), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 11$ |
3B, 11B |
$1$ |
\( 1 \) |
$0.762282639$ |
$2.072795649$ |
2.388820344 |
\( -\frac{424896929}{8} a + \frac{1123216443}{8} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -37 a + 66\) , \( -63 a - 174\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-37a+66\right){x}-63a-174$ |
| 15488.21-g4 |
15488.21-g |
$4$ |
$33$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.21 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{9} \cdot 11^{8} \) |
$2.63746$ |
$(a), (-a+1), (2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 11$ |
3B, 11B |
$1$ |
\( 3 \) |
$2.091761564$ |
$0.624971403$ |
5.929315373 |
\( -\frac{424896929}{8} a + \frac{1123216443}{8} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 489 a + 109\) , \( 661 a + 7063\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(489a+109\right){x}+661a+7063$ |
| 19602.3-b4 |
19602.3-b |
$4$ |
$33$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
19602.3 |
\( 2 \cdot 3^{4} \cdot 11^{2} \) |
\( 2^{3} \cdot 3^{12} \cdot 11^{8} \) |
$2.79745$ |
$(a), (2a+1), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 11$ |
3B.1.1, 11B |
$1$ |
\( 2 \cdot 3^{2} \) |
$6.219167594$ |
$0.294614344$ |
5.540221346 |
\( -\frac{424896929}{8} a + \frac{1123216443}{8} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -851 a - 2696\) , \( -28694 a - 50307\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-851a-2696\right){x}-28694a-50307$ |
| 29282.3-c4 |
29282.3-c |
$4$ |
$33$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
29282.3 |
\( 2 \cdot 11^{4} \) |
\( 2^{3} \cdot 11^{8} \) |
$3.09270$ |
$(a), (-2a+3), (2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 11$ |
3B, 11B.3.2 |
$1$ |
\( 3 \) |
$1$ |
$0.883843034$ |
2.004367600 |
\( -\frac{424896929}{8} a + \frac{1123216443}{8} \) |
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -58 a + 390\) , \( -1874 a + 148\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-58a+390\right){x}-1874a+148$ |
| 30976.15-b4 |
30976.15-b |
$4$ |
$33$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
30976.15 |
\( 2^{8} \cdot 11^{2} \) |
\( 2^{27} \cdot 11^{8} \) |
$3.13649$ |
$(a), (-a+1), (2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 11$ |
3B, 11B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$0.220960758$ |
1.002183800 |
\( -\frac{424896929}{8} a + \frac{1123216443}{8} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -1512 a - 4792\) , \( -62804 a - 118068\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1512a-4792\right){x}-62804a-118068$ |
*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.
