| 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 |
| 1183.1-a1 |
1183.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1183.1 |
\( 7 \cdot 13^{2} \) |
\( 7^{2} \cdot 13^{2} \) |
$2.40157$ |
$(a+3), (13)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.142392150$ |
$15.18864281$ |
1.887797308 |
\( \frac{110592}{91} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 1\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}+{x}$ |
| 1183.1-b1 |
1183.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1183.1 |
\( 7 \cdot 13^{2} \) |
\( 7^{2} \cdot 13^{2} \) |
$2.40157$ |
$(a+3), (13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$4$ |
\( 2 \) |
$1$ |
$2.103680643$ |
3.672486013 |
\( -\frac{43614208}{91} \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( 37 a - 101\) , \( 162 a - 452\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(37a-101\right){x}+162a-452$ |
| 1183.1-b2 |
1183.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1183.1 |
\( 7 \cdot 13^{2} \) |
\( 7^{18} \cdot 13^{2} \) |
$2.40157$ |
$(a+3), (13)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1 |
$4$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$2.103680643$ |
3.672486013 |
\( -\frac{178643795968}{524596891} \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( 587 a - 1641\) , \( -29288 a + 81758\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(587a-1641\right){x}-29288a+81758$ |
| 1183.1-b3 |
1183.1-b |
$3$ |
$9$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1183.1 |
\( 7 \cdot 13^{2} \) |
\( 7^{6} \cdot 13^{6} \) |
$2.40157$ |
$(a+3), (13)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$4$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$2.103680643$ |
3.672486013 |
\( \frac{224755712}{753571} \) |
\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( 63 a + 116\) , \( -950 a - 1701\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(63a+116\right){x}-950a-1701$ |
| 1183.1-c1 |
1183.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1183.1 |
\( 7 \cdot 13^{2} \) |
\( 7^{4} \cdot 13^{4} \) |
$2.40157$ |
$(a+3), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$6.172477919$ |
2.693890218 |
\( \frac{4492125}{8281} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 2 a + 7\) , \( -9 a - 14\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a+7\right){x}-9a-14$ |
| 1183.1-c2 |
1183.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1183.1 |
\( 7 \cdot 13^{2} \) |
\( 7^{2} \cdot 13^{2} \) |
$2.40157$ |
$(a+3), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$24.68991167$ |
2.693890218 |
\( \frac{421875}{91} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -3 a - 3\) , \( -2 a - 3\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a-3\right){x}-2a-3$ |
| 1183.1-d1 |
1183.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1183.1 |
\( 7 \cdot 13^{2} \) |
\( 7^{4} \cdot 13^{4} \) |
$2.40157$ |
$(a+3), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$6.172477919$ |
2.693890218 |
\( \frac{4492125}{8281} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -4 a + 9\) , \( 8 a - 23\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-4a+9\right){x}+8a-23$ |
| 1183.1-d2 |
1183.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1183.1 |
\( 7 \cdot 13^{2} \) |
\( 7^{2} \cdot 13^{2} \) |
$2.40157$ |
$(a+3), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$24.68991167$ |
2.693890218 |
\( \frac{421875}{91} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( a - 6\) , \( a - 5\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-6\right){x}+a-5$ |
| 1183.1-e1 |
1183.1-e |
$3$ |
$9$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1183.1 |
\( 7 \cdot 13^{2} \) |
\( 7^{2} \cdot 13^{2} \) |
$2.40157$ |
$(a+3), (13)$ |
$2$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$0.243054316$ |
$36.47545801$ |
1.719657357 |
\( -\frac{43614208}{91} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -7\) , \( 5\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-7{x}+5$ |
| 1183.1-e2 |
1183.1-e |
$3$ |
$9$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1183.1 |
\( 7 \cdot 13^{2} \) |
\( 7^{18} \cdot 13^{2} \) |
$2.40157$ |
$(a+3), (13)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.243054316$ |
$0.450314296$ |
1.719657357 |
\( -\frac{178643795968}{524596891} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -117\) , \( -1245\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-117{x}-1245$ |
| 1183.1-e3 |
1183.1-e |
$3$ |
$9$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1183.1 |
\( 7 \cdot 13^{2} \) |
\( 7^{6} \cdot 13^{6} \) |
$2.40157$ |
$(a+3), (13)$ |
$2$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.243054316$ |
$4.052828668$ |
1.719657357 |
\( \frac{224755712}{753571} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 13\) , \( 42\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+13{x}+42$ |
| 1183.1-f1 |
1183.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{21}) \) |
$2$ |
$[2, 0]$ |
1183.1 |
\( 7 \cdot 13^{2} \) |
\( 7^{2} \cdot 13^{2} \) |
$2.40157$ |
$(a+3), (13)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.513244526$ |
$11.14581477$ |
4.993286582 |
\( \frac{110592}{91} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -5 a + 14\) , \( 6 a - 17\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-5a+14\right){x}+6a-17$ |
*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.
