| 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 |
| 34848.3-a1 |
34848.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
34848.3 |
\( 2^{5} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{6} \cdot 3^{4} \cdot 11^{6} \) |
$3.23022$ |
$(a), (2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.928107840$ |
1.457512527 |
\( \frac{13685}{9} a - \frac{34846}{9} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -2 a + 15\) , \( 26 a - 14\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a+15\right){x}+26a-14$ |
| 34848.3-a2 |
34848.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
34848.3 |
\( 2^{5} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{9} \cdot 3^{2} \cdot 11^{6} \) |
$3.23022$ |
$(a), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.928107840$ |
1.457512527 |
\( -\frac{4913}{3} a - \frac{9826}{3} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -5 a - 11\) , \( -13 a - 19\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-5a-11\right){x}-13a-19$ |
| 34848.3-a3 |
34848.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
34848.3 |
\( 2^{5} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{12} \cdot 3^{8} \cdot 11^{6} \) |
$3.23022$ |
$(a), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.964053920$ |
1.457512527 |
\( -\frac{5525}{9} a - \frac{136882}{81} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 38 a - 20\) , \( 81 a + 74\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(38a-20\right){x}+81a+74$ |
| 34848.3-a4 |
34848.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
34848.3 |
\( 2^{5} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{9} \cdot 3^{2} \cdot 11^{6} \) |
$3.23022$ |
$(a), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.964053920$ |
1.457512527 |
\( -\frac{35168257}{3} a + \frac{48883966}{3} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -17 a + 255\) , \( 1235 a - 482\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-17a+255\right){x}+1235a-482$ |
| 34848.3-b1 |
34848.3-b |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
34848.3 |
\( 2^{5} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{9} \cdot 3^{8} \cdot 11^{8} \) |
$3.23022$ |
$(a), (2a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 3 \) |
$0.233416372$ |
$0.779330594$ |
3.300237983 |
\( -\frac{14024}{81} a - \frac{100072}{81} \) |
\( \bigl[0\) , \( -a - 1\) , \( a\) , \( 8 a - 72\) , \( 81 a - 323\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(8a-72\right){x}+81a-323$ |
| 34848.3-c1 |
34848.3-c |
$1$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
34848.3 |
\( 2^{5} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{9} \cdot 3^{8} \cdot 11^{2} \) |
$3.23022$ |
$(a), (2a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.256423742$ |
$2.584747169$ |
4.008180453 |
\( -\frac{14024}{81} a - \frac{100072}{81} \) |
\( \bigl[0\) , \( a - 1\) , \( a\) , \( 4 a\) , \( -a - 11\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a-1\right){x}^{2}+4a{x}-a-11$ |
| 34848.3-d1 |
34848.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
34848.3 |
\( 2^{5} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{6} \cdot 3^{4} \cdot 11^{8} \) |
$3.23022$ |
$(a), (2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$2.730785362$ |
$1.383334169$ |
5.711177290 |
\( -\frac{31577}{363} a + \frac{34786}{1089} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 7 a + 1\) , \( 15 a - 54\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(7a+1\right){x}+15a-54$ |
| 34848.3-d2 |
34848.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
34848.3 |
\( 2^{5} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{12} \cdot 3^{2} \cdot 11^{10} \) |
$3.23022$ |
$(a), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.365392681$ |
$0.691667084$ |
5.711177290 |
\( \frac{105966679}{14641} a + \frac{279944450}{43923} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -113 a + 106\) , \( 198 a - 804\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-113a+106\right){x}+198a-804$ |
| 34848.3-d3 |
34848.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
34848.3 |
\( 2^{5} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{9} \cdot 3^{2} \cdot 11^{7} \) |
$3.23022$ |
$(a), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$5.461570724$ |
$1.383334169$ |
5.711177290 |
\( -\frac{359177}{11} a + \frac{396314}{33} \) |
\( \bigl[a\) , \( a\) , \( 0\) , \( 32 a + 8\) , \( 15 a - 162\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(32a+8\right){x}+15a-162$ |
| 34848.3-d4 |
34848.3-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
34848.3 |
\( 2^{5} \cdot 3^{2} \cdot 11^{2} \) |
\( 2^{9} \cdot 3^{8} \cdot 11^{7} \) |
$3.23022$ |
$(a), (2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.365392681$ |
$0.691667084$ |
5.711177290 |
\( \frac{46588633}{297} a + \frac{73036934}{891} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 152 a + 101\) , \( 310 a - 1870\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(152a+101\right){x}+310a-1870$ |
*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.
