| 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-a6 |
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 |
\( \frac{14326000}{9} a + \frac{22587625}{9} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -a - 2\) , \( -1\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-a-2\right){x}-1$ |
| 81.1-c6 |
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 |
\( \frac{14326000}{9} a + \frac{22587625}{9} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -15 a - 35\) , \( -58 a - 74\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-15a-35\right){x}-58a-74$ |
| 144.4-c6 |
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 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$25.59440343$ |
0.775944329 |
\( \frac{14326000}{9} a + \frac{22587625}{9} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -13 a - 23\) , \( 40 a + 62\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-13a-23\right){x}+40a+62$ |
| 144.5-c6 |
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 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$6.398600858$ |
0.775944329 |
\( \frac{14326000}{9} a + \frac{22587625}{9} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -3 a - 11\) , \( -15 a - 26\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-3a-11\right){x}-15a-26$ |
| 576.6-e6 |
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 |
\( \frac{14326000}{9} a + \frac{22587625}{9} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -61 a - 98\) , \( -437 a - 681\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-61a-98\right){x}-437a-681$ |
| 576.6-n6 |
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 |
$1$ |
\( 2^{3} \) |
$0.419579055$ |
$18.09797622$ |
1.841701975 |
\( \frac{14326000}{9} a + \frac{22587625}{9} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 39 a - 110\) , \( -192 a + 492\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(39a-110\right){x}-192a+492$ |
| 576.7-e6 |
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 |
\( \frac{14326000}{9} a + \frac{22587625}{9} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 7 a - 29\) , \( -34 a + 35\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(7a-29\right){x}-34a+35$ |
| 576.7-n6 |
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 |
$1$ |
\( 2^{3} \) |
$1.678316222$ |
$4.524494057$ |
1.841701975 |
\( \frac{14326000}{9} a + \frac{22587625}{9} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -268 a - 420\) , \( -3824 a - 5972\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-268a-420\right){x}-3824a-5972$ |
*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.
