| 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 |
| 132.2-a1 |
132.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
132.2 |
\( 2^{2} \cdot 3 \cdot 11 \) |
\( - 2^{8} \cdot 3 \cdot 11^{12} \) |
$1.04923$ |
$(a+1), (a), (-2a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$3.494630264$ |
1.008812861 |
\( -\frac{23643538003629964}{9415285130163} a - \frac{6621159837126784}{3138428376721} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 3168 a - 5488\) , \( -58064 a + 100570\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(3168a-5488\right){x}-58064a+100570$ |
| 132.2-a2 |
132.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
132.2 |
\( 2^{2} \cdot 3 \cdot 11 \) |
\( - 2^{8} \cdot 3^{3} \cdot 11^{4} \) |
$1.04923$ |
$(a+1), (a), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$3.494630264$ |
1.008812861 |
\( -\frac{532822830316}{131769} a + \frac{102565833952}{14641} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 1558 a - 2698\) , \( 45568 a - 78926\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(1558a-2698\right){x}+45568a-78926$ |
| 132.2-a3 |
132.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
132.2 |
\( 2^{2} \cdot 3 \cdot 11 \) |
\( 2^{4} \cdot 3^{6} \cdot 11^{2} \) |
$1.04923$ |
$(a+1), (a), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$13.97852105$ |
1.008812861 |
\( -\frac{855872}{1089} a + \frac{10387984}{3267} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 103 a - 178\) , \( 694 a - 1202\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(103a-178\right){x}+694a-1202$ |
| 132.2-a4 |
132.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
132.2 |
\( 2^{2} \cdot 3 \cdot 11 \) |
\( 2^{8} \cdot 3 \cdot 11^{3} \) |
$1.04923$ |
$(a+1), (a), (-2a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$13.97852105$ |
1.008812861 |
\( -\frac{3672497349296128}{3993} a + \frac{2120317343793152}{1331} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 770 a - 1336\) , \( -15138 a + 26227\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(770a-1336\right){x}-15138a+26227$ |
| 132.2-a5 |
132.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
132.2 |
\( 2^{2} \cdot 3 \cdot 11 \) |
\( - 2^{8} \cdot 3^{12} \cdot 11 \) |
$1.04923$ |
$(a+1), (a), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$6.989260528$ |
1.008812861 |
\( \frac{106951564}{2673} a + \frac{560212688}{8019} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -232 a + 402\) , \( 3426 a - 5934\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-232a+402\right){x}+3426a-5934$ |
| 132.2-a6 |
132.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
132.2 |
\( 2^{2} \cdot 3 \cdot 11 \) |
\( 2^{8} \cdot 3^{3} \cdot 11 \) |
$1.04923$ |
$(a+1), (a), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$13.97852105$ |
1.008812861 |
\( \frac{17334272}{99} a + \frac{3506176}{11} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 10 a - 16\) , \( -18 a + 31\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(10a-16\right){x}-18a+31$ |
| 132.2-a7 |
132.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
132.2 |
\( 2^{2} \cdot 3 \cdot 11 \) |
\( 2^{4} \cdot 3^{2} \cdot 11^{6} \) |
$1.04923$ |
$(a+1), (a), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$13.97852105$ |
1.008812861 |
\( \frac{76270088859584}{5314683} a + \frac{141594074718736}{5314683} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 2683 a - 4648\) , \( -97004 a + 168016\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2683a-4648\right){x}-97004a+168016$ |
| 132.2-a8 |
132.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
132.2 |
\( 2^{2} \cdot 3 \cdot 11 \) |
\( - 2^{8} \cdot 3^{4} \cdot 11^{3} \) |
$1.04923$ |
$(a+1), (a), (-2a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$6.989260528$ |
1.008812861 |
\( \frac{9170755106790082028}{11979} a + \frac{15884213788723449968}{11979} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 2198 a - 3828\) , \( -134130 a + 232350\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2198a-3828\right){x}-134130a+232350$ |
| 132.2-b1 |
132.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
132.2 |
\( 2^{2} \cdot 3 \cdot 11 \) |
\( - 2^{8} \cdot 3 \cdot 11^{12} \) |
$1.04923$ |
$(a+1), (a), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$1.079472327$ |
1.402275687 |
\( -\frac{23643538003629964}{9415285130163} a - \frac{6621159837126784}{3138428376721} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 3168 a - 5491\) , \( 61232 a - 106060\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(3168a-5491\right){x}+61232a-106060$ |
| 132.2-b2 |
132.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
132.2 |
\( 2^{2} \cdot 3 \cdot 11 \) |
\( - 2^{8} \cdot 3^{3} \cdot 11^{4} \) |
$1.04923$ |
$(a+1), (a), (-2a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$9.715250949$ |
1.402275687 |
\( -\frac{532822830316}{131769} a + \frac{102565833952}{14641} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 1558 a - 2701\) , \( -44010 a + 76226\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(1558a-2701\right){x}-44010a+76226$ |
| 132.2-b3 |
132.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
132.2 |
\( 2^{2} \cdot 3 \cdot 11 \) |
\( 2^{4} \cdot 3^{6} \cdot 11^{2} \) |
$1.04923$ |
$(a+1), (a), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$19.43050189$ |
1.402275687 |
\( -\frac{855872}{1089} a + \frac{10387984}{3267} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 103 a - 181\) , \( -591 a + 1022\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(103a-181\right){x}-591a+1022$ |
| 132.2-b4 |
132.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
132.2 |
\( 2^{2} \cdot 3 \cdot 11 \) |
\( 2^{8} \cdot 3 \cdot 11^{3} \) |
$1.04923$ |
$(a+1), (a), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$2.158944655$ |
1.402275687 |
\( -\frac{3672497349296128}{3993} a + \frac{2120317343793152}{1331} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 770 a - 1336\) , \( 15138 a - 26227\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(770a-1336\right){x}+15138a-26227$ |
| 132.2-b5 |
132.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
132.2 |
\( 2^{2} \cdot 3 \cdot 11 \) |
\( - 2^{8} \cdot 3^{12} \cdot 11 \) |
$1.04923$ |
$(a+1), (a), (-2a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$4.857625474$ |
1.402275687 |
\( \frac{106951564}{2673} a + \frac{560212688}{8019} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -232 a + 399\) , \( -3658 a + 6334\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-232a+399\right){x}-3658a+6334$ |
| 132.2-b6 |
132.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
132.2 |
\( 2^{2} \cdot 3 \cdot 11 \) |
\( 2^{8} \cdot 3^{3} \cdot 11 \) |
$1.04923$ |
$(a+1), (a), (-2a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$19.43050189$ |
1.402275687 |
\( \frac{17334272}{99} a + \frac{3506176}{11} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 10 a - 16\) , \( 18 a - 31\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(10a-16\right){x}+18a-31$ |
| 132.2-b7 |
132.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
132.2 |
\( 2^{2} \cdot 3 \cdot 11 \) |
\( 2^{4} \cdot 3^{2} \cdot 11^{6} \) |
$1.04923$ |
$(a+1), (a), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$2.158944655$ |
1.402275687 |
\( \frac{76270088859584}{5314683} a + \frac{141594074718736}{5314683} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 2683 a - 4651\) , \( 99687 a - 172666\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(2683a-4651\right){x}+99687a-172666$ |
| 132.2-b8 |
132.2-b |
$8$ |
$12$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
132.2 |
\( 2^{2} \cdot 3 \cdot 11 \) |
\( - 2^{8} \cdot 3^{4} \cdot 11^{3} \) |
$1.04923$ |
$(a+1), (a), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$0.539736163$ |
1.402275687 |
\( \frac{9170755106790082028}{11979} a + \frac{15884213788723449968}{11979} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 2198 a - 3831\) , \( 136328 a - 236180\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(2198a-3831\right){x}+136328a-236180$ |
*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.
