| 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 |
| 196.2-a3 |
196.2-a |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
196.2 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$0.57911$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/3\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1[2] |
$1$ |
\( 2 \cdot 3^{3} \) |
$1$ |
$2.626251405$ |
0.505422318 |
\( \frac{9938375}{21952} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 4 a - 5\) , \( -6\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(4a-5\right){x}-6$ |
| 196.2-a4 |
196.2-a |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
196.2 |
\( 2^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{12} \) |
$0.57911$ |
$(-3a+1), (3a-2), (2)$ |
0 |
$\Z/3\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1[2] |
$1$ |
\( 2^{2} \cdot 3^{3} \) |
$1$ |
$1.313125702$ |
0.505422318 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -36 a + 35\) , \( -70\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-36a+35\right){x}-70$ |
| 7644.3-c5 |
7644.3-c |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7644.3 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13 \) |
\( 2^{6} \cdot 3^{6} \cdot 7^{9} \cdot 13^{6} \) |
$1.44720$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
0 |
$\Z/3\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1[2] |
$1$ |
\( 2^{3} \cdot 3^{5} \) |
$1$ |
$0.312779670$ |
2.167001122 |
\( -\frac{151053045516501325}{6814431024492} a + \frac{268398648679382443}{122659758440856} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -144 a - 751\) , \( -2113 a - 8144\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-144a-751\right){x}-2113a-8144$ |
| 7644.3-c6 |
7644.3-c |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7644.3 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13 \) |
\( 2^{12} \cdot 3^{3} \cdot 7^{9} \cdot 13^{3} \) |
$1.44720$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (2)$ |
0 |
$\Z/3\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1[2] |
$1$ |
\( 2^{2} \cdot 3^{5} \) |
$1$ |
$0.625559340$ |
2.167001122 |
\( \frac{40759196411725}{18610189416} a - \frac{46842802400791}{148881515328} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -104 a - 31\) , \( 607 a - 344\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-104a-31\right){x}+607a-344$ |
| 7644.4-c5 |
7644.4-c |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7644.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13 \) |
\( 2^{6} \cdot 3^{6} \cdot 7^{9} \cdot 13^{6} \) |
$1.44720$ |
$(-2a+1), (-3a+1), (3a-2), (4a-3), (2)$ |
0 |
$\Z/3\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1[2] |
$1$ |
\( 2^{3} \cdot 3^{5} \) |
$1$ |
$0.312779670$ |
2.167001122 |
\( \frac{151053045516501325}{6814431024492} a - \frac{2450556170617641407}{122659758440856} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 751 a + 144\) , \( 2113 a - 10257\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(751a+144\right){x}+2113a-10257$ |
| 7644.4-c6 |
7644.4-c |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7644.4 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13 \) |
\( 2^{12} \cdot 3^{3} \cdot 7^{9} \cdot 13^{3} \) |
$1.44720$ |
$(-2a+1), (-3a+1), (3a-2), (4a-3), (2)$ |
0 |
$\Z/3\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1[2] |
$1$ |
\( 2^{2} \cdot 3^{5} \) |
$1$ |
$0.625559340$ |
2.167001122 |
\( -\frac{40759196411725}{18610189416} a + \frac{279230768893009}{148881515328} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 31 a + 104\) , \( -607 a + 263\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(31a+104\right){x}-607a+263$ |
| 145236.5-h4 |
145236.5-h |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
145236.5 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13 \cdot 19 \) |
\( 2^{12} \cdot 3^{6} \cdot 7^{9} \cdot 13^{3} \cdot 19^{3} \) |
$3.02147$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (-5a+3), (2)$ |
$1$ |
$\Z/3\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1[2] |
$1$ |
\( 2^{3} \cdot 3^{6} \) |
$0.738495705$ |
$0.215226588$ |
6.607174312 |
\( -\frac{236498988514950625}{42549096401448} a - \frac{4972546796420537875}{3063534940904256} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 674 a + 890\) , \( 20190 a - 21733\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(674a+890\right){x}+20190a-21733$ |
| 145236.5-h5 |
145236.5-h |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
145236.5 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13 \cdot 19 \) |
\( 2^{6} \cdot 3^{3} \cdot 7^{9} \cdot 13^{6} \cdot 19^{6} \) |
$3.02147$ |
$(-2a+1), (-3a+1), (3a-2), (-4a+1), (-5a+3), (2)$ |
$1$ |
$\Z/3\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1[2] |
$1$ |
\( 2^{3} \cdot 3^{6} \) |
$1.476991411$ |
$0.107613294$ |
6.607174312 |
\( \frac{130546127259131404211375}{480886366591438076178} a - \frac{2361227210068147643544625}{1923545466365752304712} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -3766 a + 2930\) , \( 35790 a - 137029\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-3766a+2930\right){x}+35790a-137029$ |
| 145236.8-h3 |
145236.8-h |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
145236.8 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13 \cdot 19 \) |
\( 2^{12} \cdot 3^{6} \cdot 7^{9} \cdot 13^{3} \cdot 19^{3} \) |
$3.02147$ |
$(-2a+1), (-3a+1), (3a-2), (4a-3), (-5a+2), (2)$ |
$1$ |
$\Z/3\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1[2] |
$1$ |
\( 2^{3} \cdot 3^{6} \) |
$0.738495705$ |
$0.215226588$ |
6.607174312 |
\( \frac{236498988514950625}{42549096401448} a - \frac{22000473969496982875}{3063534940904256} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 1565 a - 891\) , \( -20190 a - 1543\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(1565a-891\right){x}-20190a-1543$ |
| 145236.8-h4 |
145236.8-h |
$10$ |
$18$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
145236.8 |
\( 2^{2} \cdot 3 \cdot 7^{2} \cdot 13 \cdot 19 \) |
\( 2^{6} \cdot 3^{3} \cdot 7^{9} \cdot 13^{6} \cdot 19^{6} \) |
$3.02147$ |
$(-2a+1), (-3a+1), (3a-2), (4a-3), (-5a+2), (2)$ |
$1$ |
$\Z/3\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Cs.1.1[2] |
$1$ |
\( 2^{3} \cdot 3^{6} \) |
$1.476991411$ |
$0.107613294$ |
6.607174312 |
\( -\frac{130546127259131404211375}{480886366591438076178} a - \frac{1839042701031622026699125}{1923545466365752304712} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -835 a - 2931\) , \( -35790 a - 101239\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-835a-2931\right){x}-35790a-101239$ |
*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.
