| 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 |
| 142884.2-a1 |
142884.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
142884.2 |
\( 2^{2} \cdot 3^{6} \cdot 7^{2} \) |
\( 2^{14} \cdot 3^{8} \cdot 7^{4} \) |
$3.00916$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2^{2} \cdot 3 \cdot 7 \) |
$0.010953522$ |
$1.563396762$ |
6.644031204 |
\( \frac{934407}{6272} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 9\) , \( -35\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+9{x}-35$ |
| 142884.2-b1 |
142884.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
142884.2 |
\( 2^{2} \cdot 3^{6} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 7^{4} \) |
$3.00916$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2^{4} \) |
$0.139040891$ |
$1.015635933$ |
5.217950435 |
\( -\frac{15590912409}{784} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 225 a\) , \( 1357\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+225a{x}+1357$ |
| 142884.2-c1 |
142884.2-c |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
142884.2 |
\( 2^{2} \cdot 3^{6} \cdot 7^{2} \) |
\( 2^{24} \cdot 3^{12} \cdot 7^{4} \) |
$3.00916$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$0.246068540$ |
$0.602839948$ |
5.481222905 |
\( -\frac{60698457}{200704} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -74 a + 73\) , \( 649\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-74a+73\right){x}+649$ |
| 142884.2-c2 |
142884.2-c |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
142884.2 |
\( 2^{2} \cdot 3^{6} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 7^{12} \) |
$3.00916$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 2^{4} \cdot 3^{3} \) |
$0.082022846$ |
$0.602839948$ |
5.481222905 |
\( \frac{505636983}{1882384} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 72 a - 72\) , \( 528\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(72a-72\right){x}+528$ |
| 142884.2-d1 |
142884.2-d |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
142884.2 |
\( 2^{2} \cdot 3^{6} \cdot 7^{2} \) |
\( 2^{18} \cdot 3^{8} \cdot 7^{5} \) |
$3.00916$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 2 \cdot 3^{4} \) |
$0.131498954$ |
$1.041634712$ |
5.693897079 |
\( \frac{62093313}{87808} a - \frac{28663011}{175616} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -36 a + 22\) , \( -12 a - 103\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-36a+22\right){x}-12a-103$ |
| 142884.2-d2 |
142884.2-d |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
142884.2 |
\( 2^{2} \cdot 3^{6} \cdot 7^{2} \) |
\( 2^{6} \cdot 3^{12} \cdot 7^{7} \) |
$3.00916$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 2 \cdot 3^{3} \) |
$0.394496862$ |
$1.041634712$ |
5.693897079 |
\( -\frac{728867241}{941192} a + \frac{343966635}{941192} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 36 a - 24\) , \( -72 a - 64\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(36a-24\right){x}-72a-64$ |
| 142884.2-e1 |
142884.2-e |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
142884.2 |
\( 2^{2} \cdot 3^{6} \cdot 7^{2} \) |
\( 2^{6} \cdot 3^{12} \cdot 7^{7} \) |
$3.00916$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 2 \cdot 3^{3} \) |
$0.394496862$ |
$1.041634712$ |
5.693897079 |
\( \frac{728867241}{941192} a - \frac{192450303}{470596} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 12 a + 24\) , \( 72 a - 136\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(12a+24\right){x}+72a-136$ |
| 142884.2-e2 |
142884.2-e |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
142884.2 |
\( 2^{2} \cdot 3^{6} \cdot 7^{2} \) |
\( 2^{18} \cdot 3^{8} \cdot 7^{5} \) |
$3.00916$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 2 \cdot 3^{4} \) |
$0.131498954$ |
$1.041634712$ |
5.693897079 |
\( -\frac{62093313}{87808} a + \frac{95523615}{175616} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -14 a - 23\) , \( 12 a - 115\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-14a-23\right){x}+12a-115$ |
| 142884.2-f1 |
142884.2-f |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
142884.2 |
\( 2^{2} \cdot 3^{6} \cdot 7^{2} \) |
\( 2^{6} \cdot 3^{12} \cdot 7^{2} \) |
$3.00916$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{2} \) |
$1$ |
$2.231183039$ |
2.576348256 |
\( -\frac{185193}{56} \) |
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -11 a + 10\) , \( 19\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-11a+10\right){x}+19$ |
| 142884.2-f2 |
142884.2-f |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
142884.2 |
\( 2^{2} \cdot 3^{6} \cdot 7^{2} \) |
\( 2^{2} \cdot 3^{8} \cdot 7^{6} \) |
$3.00916$ |
$(-2a+1), (-3a+1), (3a-2), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3^{2} \) |
$1$ |
$2.231183039$ |
2.576348256 |
\( \frac{934407}{686} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 9 a - 9\) , \( 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(9a-9\right){x}+3$ |
*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.
