| 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 |
| 9.1-a5 |
9.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$0.63815$ |
$(3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$31.97784377$ |
0.969470791 |
\( -\frac{14326000}{9} a + \frac{36913625}{9} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 2 a - 4\) , \( -2 a + 3\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a-4\right){x}-2a+3$ |
| 81.1-c5 |
81.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
81.1 |
\( 3^{4} \) |
\( 3^{16} \) |
$1.10531$ |
$(3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$6.828410025$ |
0.414033173 |
\( -\frac{14326000}{9} a + \frac{36913625}{9} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 15 a - 50\) , \( 58 a - 132\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(15a-50\right){x}+58a-132$ |
| 144.4-c5 |
144.4-c |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
144.4 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{4} \) |
$1.27630$ |
$(-a+2), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$6.398600858$ |
0.775944329 |
\( -\frac{14326000}{9} a + \frac{36913625}{9} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 5 a - 12\) , \( 4 a - 28\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(5a-12\right){x}+4a-28$ |
| 144.5-c5 |
144.5-c |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
144.5 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{4} \) |
$1.27630$ |
$(-a-1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$25.59440343$ |
0.775944329 |
\( -\frac{14326000}{9} a + \frac{36913625}{9} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 11 a - 36\) , \( -41 a + 102\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(11a-36\right){x}-41a+102$ |
| 576.6-e5 |
576.6-e |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
576.6 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{4} \) |
$1.80496$ |
$(-a-1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.956971041$ |
$7.242622550$ |
3.437603564 |
\( -\frac{14326000}{9} a + \frac{36913625}{9} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -4 a - 21\) , \( 11 a + 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a-21\right){x}+11a+4$ |
| 576.6-n5 |
576.6-n |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
576.6 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{4} \) |
$1.80496$ |
$(-a-1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.678316222$ |
$4.524494057$ |
1.841701975 |
\( -\frac{14326000}{9} a + \frac{36913625}{9} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 271 a - 686\) , \( 3406 a - 8718\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(271a-686\right){x}+3406a-8718$ |
| 576.7-e5 |
576.7-e |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
576.7 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{4} \) |
$1.80496$ |
$(-a+2), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.956971041$ |
$7.242622550$ |
3.437603564 |
\( -\frac{14326000}{9} a + \frac{36913625}{9} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 59 a - 157\) , \( 436 a - 1117\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(59a-157\right){x}+436a-1117$ |
| 576.7-n5 |
576.7-n |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
576.7 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{4} \) |
$1.80496$ |
$(-a+2), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.419579055$ |
$18.09797622$ |
1.841701975 |
\( -\frac{14326000}{9} a + \frac{36913625}{9} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -41 a - 69\) , \( 191 a + 301\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-41a-69\right){x}+191a+301$ |
*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.
