| 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 |
| 1116.2-a2 |
1116.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
1116.2 |
\( 2^{2} \cdot 3^{2} \cdot 31 \) |
\( 2^{6} \cdot 3^{6} \cdot 31 \) |
$0.89457$ |
$(-2a+1), (6a-5), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1[2] |
$1$ |
\( 3 \) |
$1$ |
$2.908714005$ |
1.119564542 |
\( -\frac{44272737}{124} a + \frac{99194139}{248} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -6 a - 12\) , \( -12 a - 12\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-6a-12\right){x}-12a-12$ |
| 3844.3-a2 |
3844.3-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
3844.3 |
\( 2^{2} \cdot 31^{2} \) |
\( 2^{6} \cdot 31^{7} \) |
$1.21869$ |
$(6a-5), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \) |
$1$ |
$0.904858775$ |
2.089681829 |
\( -\frac{44272737}{124} a + \frac{99194139}{248} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 3 a + 164\) , \( -963 a + 439\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(3a+164\right){x}-963a+439$ |
| 6076.2-a2 |
6076.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
6076.2 |
\( 2^{2} \cdot 7^{2} \cdot 31 \) |
\( 2^{6} \cdot 7^{6} \cdot 31 \) |
$1.36648$ |
$(-3a+1), (6a-5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \) |
$0.144579652$ |
$1.904200300$ |
1.271596037 |
\( -\frac{44272737}{124} a + \frac{99194139}{248} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 38 a + 1\) , \( 43 a - 113\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(38a+1\right){x}+43a-113$ |
| 6076.6-b2 |
6076.6-b |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
6076.6 |
\( 2^{2} \cdot 7^{2} \cdot 31 \) |
\( 2^{6} \cdot 7^{6} \cdot 31 \) |
$1.36648$ |
$(3a-2), (6a-5), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 1 \) |
$1$ |
$1.904200300$ |
2.198781112 |
\( -\frac{44272737}{124} a + \frac{99194139}{248} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -28 a - 14\) , \( -76 a + 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-28a-14\right){x}-76a+4$ |
| 7936.2-a2 |
7936.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7936.2 |
\( 2^{8} \cdot 31 \) |
\( 2^{30} \cdot 31 \) |
$1.46083$ |
$(6a-5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2^{2} \) |
$0.115536819$ |
$1.259510110$ |
1.344254264 |
\( -\frac{44272737}{124} a + \frac{99194139}{248} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 66 a - 97\) , \( 321 a - 353\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(66a-97\right){x}+321a-353$ |
| 7936.2-e2 |
7936.2-e |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7936.2 |
\( 2^{8} \cdot 31 \) |
\( 2^{30} \cdot 31 \) |
$1.46083$ |
$(6a-5), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \) |
$1$ |
$1.259510110$ |
2.908714005 |
\( -\frac{44272737}{124} a + \frac{99194139}{248} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 66 a - 97\) , \( -321 a + 353\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(66a-97\right){x}-321a+353$ |
| 44764.2-a2 |
44764.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
44764.2 |
\( 2^{2} \cdot 19^{2} \cdot 31 \) |
\( 2^{6} \cdot 19^{6} \cdot 31 \) |
$2.25129$ |
$(-5a+3), (6a-5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \cdot 3 \) |
$0.151308051$ |
$1.155805745$ |
2.423245982 |
\( -\frac{44272737}{124} a + \frac{99194139}{248} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -63 a - 54\) , \( 354 a + 123\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-63a-54\right){x}+354a+123$ |
| 44764.6-a2 |
44764.6-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
44764.6 |
\( 2^{2} \cdot 19^{2} \cdot 31 \) |
\( 2^{6} \cdot 19^{6} \cdot 31 \) |
$2.25129$ |
$(-5a+2), (6a-5), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 3 \) |
$1$ |
$1.155805745$ |
4.003828548 |
\( -\frac{44272737}{124} a + \frac{99194139}{248} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -13 a - 95\) , \( 79 a + 387\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-13a-95\right){x}+79a+387$ |
| 71424.2-d2 |
71424.2-d |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
71424.2 |
\( 2^{8} \cdot 3^{2} \cdot 31 \) |
\( 2^{30} \cdot 3^{6} \cdot 31 \) |
$2.53023$ |
$(-2a+1), (6a-5), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \) |
$1$ |
$0.727178501$ |
1.679346813 |
\( -\frac{44272737}{124} a + \frac{99194139}{248} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -195 a + 291\) , \( 864 a + 962\bigr] \) |
${y}^2={x}^{3}+\left(-195a+291\right){x}+864a+962$ |
| 119164.2-a2 |
119164.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
119164.2 |
\( 2^{2} \cdot 31^{3} \) |
\( 2^{6} \cdot 31^{7} \) |
$2.87565$ |
$(-6a+1), (6a-5), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 1 \) |
$1$ |
$0.904858775$ |
1.044840914 |
\( -\frac{44272737}{124} a + \frac{99194139}{248} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( 114 a + 76\) , \( 511 a - 986\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(114a+76\right){x}+511a-986$ |
| 126976.2-a2 |
126976.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
126976.2 |
\( 2^{12} \cdot 31 \) |
\( 2^{42} \cdot 31 \) |
$2.92166$ |
$(6a-5), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2 \) |
$1$ |
$0.629755055$ |
1.454357002 |
\( -\frac{44272737}{124} a + \frac{99194139}{248} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 261 a - 388\) , \( -2434 a + 2175\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(261a-388\right){x}-2434a+2175$ |
| 126976.2-j2 |
126976.2-j |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
126976.2 |
\( 2^{12} \cdot 31 \) |
\( 2^{42} \cdot 31 \) |
$2.92166$ |
$(6a-5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B[2] |
$1$ |
\( 2^{2} \) |
$1.242951212$ |
$0.629755055$ |
7.230779196 |
\( -\frac{44272737}{124} a + \frac{99194139}{248} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -387 a + 128\) , \( 2694 a - 2563\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-387a+128\right){x}+2694a-2563$ |
*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.
