| 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 |
| 1458.1-a1 |
1458.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{9} \cdot 3^{22} \) |
$1.10435$ |
$(a+1), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$0.699423429$ |
0.699423429 |
\( -\frac{23376651}{32} a - \frac{13799643}{32} \) |
\( \bigl[1\) , \( -1\) , \( i + 1\) , \( 283 i + 133\) , \( -338 i - 2152\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(283i+133\right){x}-338i-2152$ |
| 1458.1-a2 |
1458.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{3} \cdot 3^{18} \) |
$1.10435$ |
$(a+1), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$1$ |
$2.098270288$ |
0.699423429 |
\( \frac{18333}{4} a + \frac{8019}{4} \) |
\( \bigl[1\) , \( -1\) , \( i + 1\) , \( 13 i - 2\) , \( 13 i + 8\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(13i-2\right){x}+13i+8$ |
| 1458.1-a3 |
1458.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2 \cdot 3^{6} \) |
$1.10435$ |
$(a+1), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$6.294810866$ |
0.699423429 |
\( -\frac{11691}{2} a + \frac{65637}{2} \) |
\( \bigl[1\) , \( -1\) , \( i + 1\) , \( -2 i - 2\) , \( i + 1\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(-2i-2\right){x}+i+1$ |
| 1458.1-b1 |
1458.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{9} \cdot 3^{22} \) |
$1.10435$ |
$(a+1), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$0.699423429$ |
0.699423429 |
\( \frac{23376651}{32} a - \frac{13799643}{32} \) |
\( \bigl[1\) , \( -1\) , \( i + 1\) , \( -284 i + 133\) , \( 337 i - 2152\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(-284i+133\right){x}+337i-2152$ |
| 1458.1-b2 |
1458.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{3} \cdot 3^{18} \) |
$1.10435$ |
$(a+1), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$1$ |
$2.098270288$ |
0.699423429 |
\( -\frac{18333}{4} a + \frac{8019}{4} \) |
\( \bigl[1\) , \( -1\) , \( i + 1\) , \( -14 i - 2\) , \( -14 i + 8\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(-14i-2\right){x}-14i+8$ |
| 1458.1-b3 |
1458.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2 \cdot 3^{6} \) |
$1.10435$ |
$(a+1), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$6.294810866$ |
0.699423429 |
\( \frac{11691}{2} a + \frac{65637}{2} \) |
\( \bigl[1\) , \( -1\) , \( i + 1\) , \( i - 2\) , \( -2 i + 1\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(i-2\right){x}-2i+1$ |
| 1458.1-c1 |
1458.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{2} \cdot 3^{6} \) |
$1.10435$ |
$(a+1), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$5.635135226$ |
1.252252272 |
\( -\frac{132651}{2} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-3{x}+3$ |
| 1458.1-c2 |
1458.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{18} \cdot 3^{22} \) |
$1.10435$ |
$(a+1), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$0.626126136$ |
1.252252272 |
\( -\frac{1167051}{512} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -123\) , \( -667\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-123{x}-667$ |
| 1458.1-c3 |
1458.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{6} \cdot 3^{18} \) |
$1.10435$ |
$(a+1), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$1.878378408$ |
1.252252272 |
\( \frac{9261}{8} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 12\) , \( 8\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+12{x}+8$ |
| 1458.1-d1 |
1458.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{2} \cdot 3^{18} \) |
$1.10435$ |
$(a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$0.077107140$ |
$1.878378408$ |
1.738036644 |
\( -\frac{132651}{2} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -28\) , \( 53\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-28{x}+53$ |
| 1458.1-d2 |
1458.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{18} \cdot 3^{10} \) |
$1.10435$ |
$(a+1), (3)$ |
$1$ |
$\Z/9\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{3} \) |
$0.693964260$ |
$1.878378408$ |
1.738036644 |
\( -\frac{1167051}{512} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( -13\) , \( -29\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}-13{x}-29$ |
| 1458.1-d3 |
1458.1-d |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{6} \cdot 3^{6} \) |
$1.10435$ |
$(a+1), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.231321420$ |
$5.635135226$ |
1.738036644 |
\( \frac{9261}{8} \) |
\( \bigl[i\) , \( 1\) , \( i\) , \( 2\) , \( 1\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}+2{x}+1$ |
| 1458.1-e1 |
1458.1-e |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{9} \cdot 3^{10} \) |
$1.10435$ |
$(a+1), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$2.098270288$ |
2.098270288 |
\( \frac{23376651}{32} a - \frac{13799643}{32} \) |
\( \bigl[i\) , \( 1\) , \( 1\) , \( -32 i + 15\) , \( 2 i - 75\bigr] \) |
${y}^2+i{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-32i+15\right){x}+2i-75$ |
| 1458.1-e2 |
1458.1-e |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{3} \cdot 3^{6} \) |
$1.10435$ |
$(a+1), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$1$ |
$6.294810866$ |
2.098270288 |
\( -\frac{18333}{4} a + \frac{8019}{4} \) |
\( \bigl[i\) , \( 1\) , \( 1\) , \( -2 i\) , \( -i\bigr] \) |
${y}^2+i{x}{y}+{y}={x}^{3}+{x}^{2}-2i{x}-i$ |
| 1458.1-e3 |
1458.1-e |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2 \cdot 3^{18} \) |
$1.10435$ |
$(a+1), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$2.098270288$ |
2.098270288 |
\( \frac{11691}{2} a + \frac{65637}{2} \) |
\( \bigl[i\) , \( 1\) , \( 1\) , \( 13 i - 15\) , \( -27 i + 12\bigr] \) |
${y}^2+i{x}{y}+{y}={x}^{3}+{x}^{2}+\left(13i-15\right){x}-27i+12$ |
| 1458.1-f1 |
1458.1-f |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{9} \cdot 3^{10} \) |
$1.10435$ |
$(a+1), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$2.098270288$ |
2.098270288 |
\( -\frac{23376651}{32} a - \frac{13799643}{32} \) |
\( \bigl[i\) , \( 1\) , \( 1\) , \( 31 i + 15\) , \( -2 i - 75\bigr] \) |
${y}^2+i{x}{y}+{y}={x}^{3}+{x}^{2}+\left(31i+15\right){x}-2i-75$ |
| 1458.1-f2 |
1458.1-f |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2^{3} \cdot 3^{6} \) |
$1.10435$ |
$(a+1), (3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Cs.1.1 |
$1$ |
\( 3 \) |
$1$ |
$6.294810866$ |
2.098270288 |
\( \frac{18333}{4} a + \frac{8019}{4} \) |
\( \bigl[i\) , \( 1\) , \( 1\) , \( i\) , \( i\bigr] \) |
${y}^2+i{x}{y}+{y}={x}^{3}+{x}^{2}+i{x}+i$ |
| 1458.1-f3 |
1458.1-f |
$3$ |
$9$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1458.1 |
\( 2 \cdot 3^{6} \) |
\( 2 \cdot 3^{18} \) |
$1.10435$ |
$(a+1), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$2.098270288$ |
2.098270288 |
\( -\frac{11691}{2} a + \frac{65637}{2} \) |
\( \bigl[i\) , \( 1\) , \( 1\) , \( -14 i - 15\) , \( 27 i + 12\bigr] \) |
${y}^2+i{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-14i-15\right){x}+27i+12$ |
*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.
