| 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 |
| 26.1-a1 |
26.1-a |
$2$ |
$7$ |
\(\Q(\sqrt{-182}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{2} \cdot 13^{26} \) |
$5.44437$ |
$(2,a), (13,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.6.1 |
$1$ |
\( 2^{2} \) |
$1.383448027$ |
$1.120257005$ |
0.459520419 |
\( -\frac{1064019559329}{125497034} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -35944\) , \( -2868878\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-35944{x}-2868878$ |
| 26.1-a2 |
26.1-a |
$2$ |
$7$ |
\(\Q(\sqrt{-182}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{14} \cdot 13^{14} \) |
$5.44437$ |
$(2,a), (13,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.6.1 |
$1$ |
\( 2^{2} \) |
$0.197635432$ |
$7.841799039$ |
0.459520419 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -454\) , \( 5812\bigr] \) |
${y}^2+{x}{y}={x}^3-{x}^2-454{x}+5812$ |
| 26.1-b1 |
26.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-182}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{18} \cdot 7^{12} \cdot 13^{2} \) |
$5.44437$ |
$(2,a), (13,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$7.626203082$ |
$1.793868261$ |
4.056235947 |
\( -\frac{10730978619193}{6656} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -22516\) , \( 1291088\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2-22516{x}+1291088$ |
| 26.1-b2 |
26.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-182}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{6} \cdot 7^{12} \cdot 13^{6} \) |
$5.44437$ |
$(2,a), (13,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$2.542067694$ |
$5.381604785$ |
4.056235947 |
\( -\frac{10218313}{17576} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -221\) , \( 2437\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2-221{x}+2437$ |
| 26.1-b3 |
26.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{-182}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{2} \cdot 7^{12} \cdot 13^{2} \) |
$5.44437$ |
$(2,a), (13,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$0.847355898$ |
$16.14481435$ |
4.056235947 |
\( \frac{12167}{26} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 24\) , \( -62\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2+24{x}-62$ |
| 26.1-c1 |
26.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{-182}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{18} \cdot 13^{2} \) |
$5.44437$ |
$(2,a), (13,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$9$ |
\( 2^{2} \) |
$1$ |
$1.793868261$ |
2.393466521 |
\( -\frac{10730978619193}{6656} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -460\) , \( -3830\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-460{x}-3830$ |
| 26.1-c2 |
26.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{-182}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{6} \cdot 13^{6} \) |
$5.44437$ |
$(2,a), (13,a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$9$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$5.381604785$ |
2.393466521 |
\( -\frac{10218313}{17576} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -5\) , \( -8\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-5{x}-8$ |
| 26.1-c3 |
26.1-c |
$3$ |
$9$ |
\(\Q(\sqrt{-182}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{2} \cdot 13^{2} \) |
$5.44437$ |
$(2,a), (13,a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$9$ |
\( 2^{2} \) |
$1$ |
$16.14481435$ |
2.393466521 |
\( \frac{12167}{26} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3$ |
| 26.1-d1 |
26.1-d |
$2$ |
$7$ |
\(\Q(\sqrt{-182}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{14} \cdot 13^{14} \) |
$5.44437$ |
$(2,a), (13,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.6.1 |
$9$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$1.120257005$ |
10.46291072 |
\( -\frac{1064019559329}{125497034} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -39\) , \( -971\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2-39{x}-971$ |
| 26.1-d2 |
26.1-d |
$2$ |
$7$ |
\(\Q(\sqrt{-182}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{26} \cdot 13^{2} \) |
$5.44437$ |
$(2,a), (13,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.6.1 |
$9$ |
\( 2^{2} \) |
$1$ |
$7.841799039$ |
10.46291072 |
\( -\frac{2146689}{1664} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 801\) , \( -3491\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+801{x}-3491$ |
| 26.1-e1 |
26.1-e |
$2$ |
$7$ |
\(\Q(\sqrt{-182}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{2} \cdot 13^{14} \) |
$5.44437$ |
$(2,a), (13,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$4$ |
\( 2^{2} \) |
$1$ |
$1.120257005$ |
0.664311791 |
\( -\frac{1064019559329}{125497034} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -213\) , \( -1257\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-213{x}-1257$ |
| 26.1-e2 |
26.1-e |
$2$ |
$7$ |
\(\Q(\sqrt{-182}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{14} \cdot 13^{2} \) |
$5.44437$ |
$(2,a), (13,a)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$4$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$7.841799039$ |
0.664311791 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-3{x}+3$ |
| 26.1-f1 |
26.1-f |
$3$ |
$9$ |
\(\Q(\sqrt{-182}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{30} \cdot 13^{2} \) |
$5.44437$ |
$(2,a), (13,a)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.928016098$ |
$1.793868261$ |
8.884701856 |
\( -\frac{10730978619193}{6656} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -1087\) , \( -6285\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-1087{x}-6285$ |
| 26.1-f2 |
26.1-f |
$3$ |
$9$ |
\(\Q(\sqrt{-182}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{18} \cdot 13^{6} \) |
$5.44437$ |
$(2,a), (13,a)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.928016098$ |
$5.381604785$ |
8.884701856 |
\( -\frac{10218313}{17576} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 733\) , \( -3009\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+733{x}-3009$ |
| 26.1-f3 |
26.1-f |
$3$ |
$9$ |
\(\Q(\sqrt{-182}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{14} \cdot 13^{2} \) |
$5.44437$ |
$(2,a), (13,a)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$0.928016098$ |
$16.14481435$ |
8.884701856 |
\( \frac{12167}{26} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 753\) , \( -3245\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+753{x}-3245$ |
| 26.1-g1 |
26.1-g |
$3$ |
$9$ |
\(\Q(\sqrt{-182}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{18} \cdot 13^{14} \) |
$5.44437$ |
$(2,a), (13,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$2.284397626$ |
$1.793868261$ |
10.93525848 |
\( -\frac{10730978619193}{6656} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -77659\) , \( -8336303\bigr] \) |
${y}^2+{x}{y}={x}^3-77659{x}-8336303$ |
| 26.1-g2 |
26.1-g |
$3$ |
$9$ |
\(\Q(\sqrt{-182}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{6} \cdot 13^{18} \) |
$5.44437$ |
$(2,a), (13,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.761465875$ |
$5.381604785$ |
10.93525848 |
\( -\frac{10218313}{17576} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -764\) , \( -16264\bigr] \) |
${y}^2+{x}{y}={x}^3-764{x}-16264$ |
| 26.1-g3 |
26.1-g |
$3$ |
$9$ |
\(\Q(\sqrt{-182}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{2} \cdot 13^{14} \) |
$5.44437$ |
$(2,a), (13,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2^{2} \) |
$2.284397626$ |
$16.14481435$ |
10.93525848 |
\( \frac{12167}{26} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 81\) , \( 467\bigr] \) |
${y}^2+{x}{y}={x}^3+81{x}+467$ |
| 26.1-h1 |
26.1-h |
$2$ |
$7$ |
\(\Q(\sqrt{-182}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{2} \cdot 7^{12} \cdot 13^{14} \) |
$5.44437$ |
$(2,a), (13,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.6 |
$1$ |
\( 2^{2} \cdot 7 \) |
$14.35077864$ |
$1.120257005$ |
33.36687018 |
\( -\frac{1064019559329}{125497034} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -10422\) , \( 451903\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-10422{x}+451903$ |
| 26.1-h2 |
26.1-h |
$2$ |
$7$ |
\(\Q(\sqrt{-182}) \) |
$2$ |
$[0, 1]$ |
26.1 |
\( 2 \cdot 13 \) |
\( 2^{14} \cdot 7^{12} \cdot 13^{2} \) |
$5.44437$ |
$(2,a), (13,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.6 |
$1$ |
\( 2^{2} \cdot 7 \) |
$2.050111235$ |
$7.841799039$ |
33.36687018 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -132\) , \( -857\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}^2-132{x}-857$ |
*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.
