| 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 |
| 338.2-a1 |
338.2-a |
$3$ |
$9$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
338.2 |
\( 2 \cdot 13^{2} \) |
\( 2^{30} \cdot 13^{2} \) |
$2.86722$ |
$(2,a), (13,a+5), (13,a+8)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2 \) |
$2.977948821$ |
$0.896934130$ |
2.855444699 |
\( -\frac{10730978619193}{6656} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -1829\) , \( -28797\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-1829{x}-28797$ |
| 338.2-a2 |
338.2-a |
$3$ |
$9$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
338.2 |
\( 2 \cdot 13^{2} \) |
\( 2^{18} \cdot 13^{6} \) |
$2.86722$ |
$(2,a), (13,a+5), (13,a+8)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2 \) |
$0.992649607$ |
$2.690802392$ |
2.855444699 |
\( -\frac{10218313}{17576} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -9\) , \( -41\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-9{x}-41$ |
| 338.2-a3 |
338.2-a |
$3$ |
$9$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
338.2 |
\( 2 \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$2.86722$ |
$(2,a), (13,a+5), (13,a+8)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2 \) |
$0.330883202$ |
$8.072407178$ |
2.855444699 |
\( \frac{12167}{26} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 11\) , \( 3\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+11{x}+3$ |
| 338.2-b1 |
338.2-b |
$3$ |
$9$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
338.2 |
\( 2 \cdot 13^{2} \) |
\( 2^{18} \cdot 13^{2} \) |
$2.86722$ |
$(2,a), (13,a+5), (13,a+8)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \) |
$2.284397626$ |
$0.896934130$ |
2.190424175 |
\( -\frac{10730978619193}{6656} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -460\) , \( -3830\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-460{x}-3830$ |
| 338.2-b2 |
338.2-b |
$3$ |
$9$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
338.2 |
\( 2 \cdot 13^{2} \) |
\( 2^{6} \cdot 13^{6} \) |
$2.86722$ |
$(2,a), (13,a+5), (13,a+8)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.761465875$ |
$2.690802392$ |
2.190424175 |
\( -\frac{10218313}{17576} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -5\) , \( -8\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-5{x}-8$ |
| 338.2-b3 |
338.2-b |
$3$ |
$9$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
338.2 |
\( 2 \cdot 13^{2} \) |
\( 2^{2} \cdot 13^{2} \) |
$2.86722$ |
$(2,a), (13,a+5), (13,a+8)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \) |
$2.284397626$ |
$8.072407178$ |
2.190424175 |
\( \frac{12167}{26} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3$ |
| 338.2-c1 |
338.2-c |
$2$ |
$7$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
338.2 |
\( 2 \cdot 13^{2} \) |
\( 2^{2} \cdot 13^{14} \) |
$2.86722$ |
$(2,a), (13,a+5), (13,a+8)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$0.560128502$ |
0.299401278 |
\( -\frac{1064019559329}{125497034} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -213\) , \( -1257\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-213{x}-1257$ |
| 338.2-c2 |
338.2-c |
$2$ |
$7$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
338.2 |
\( 2 \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{2} \) |
$2.86722$ |
$(2,a), (13,a+5), (13,a+8)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$3.920899519$ |
0.299401278 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 338.2-d1 |
338.2-d |
$2$ |
$7$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
338.2 |
\( 2 \cdot 13^{2} \) |
\( 2^{14} \cdot 13^{14} \) |
$2.86722$ |
$(2,a), (13,a+5), (13,a+8)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.6 |
$1$ |
\( 2 \cdot 7^{2} \) |
$1$ |
$0.560128502$ |
14.67066265 |
\( -\frac{1064019559329}{125497034} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -837\) , \( -9203\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2-837{x}-9203$ |
| 338.2-d2 |
338.2-d |
$2$ |
$7$ |
\(\Q(\sqrt{-14}) \) |
$2$ |
$[0, 1]$ |
338.2 |
\( 2 \cdot 13^{2} \) |
\( 2^{26} \cdot 13^{2} \) |
$2.86722$ |
$(2,a), (13,a+5), (13,a+8)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.6 |
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$3.920899519$ |
14.67066265 |
\( -\frac{2146689}{1664} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 3\) , \( 37\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+3{x}+37$ |
*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.
