| 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-b1 |
9.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{10} \) |
$0.63815$ |
$(3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$0.808547756$ |
0.196101635 |
\( -\frac{13549359104}{243} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( 795 a - 2035\) , \( 17928 a - 45924\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(795a-2035\right){x}+17928a-45924$ |
| 81.1-a1 |
81.1-a |
$2$ |
$5$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
81.1 |
\( 3^{4} \) |
\( 3^{22} \) |
$1.10531$ |
$(3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2 \) |
$1$ |
$8.687738250$ |
4.214172053 |
\( -\frac{13549359104}{243} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 7152 a - 18327\) , \( -472886 a + 1211329\bigr] \) |
${y}^2+{y}={x}^{3}+\left(7152a-18327\right){x}-472886a+1211329$ |
| 144.4-a1 |
144.4-a |
$2$ |
$5$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
144.4 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{10} \) |
$1.27630$ |
$(-a+2), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 5 \) |
$1$ |
$2.295286137$ |
2.783443290 |
\( -\frac{13549359104}{243} \) |
\( \bigl[0\) , \( -a - 1\) , \( a\) , \( 1938 a - 4965\) , \( -66328 a + 169901\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(1938a-4965\right){x}-66328a+169901$ |
| 144.5-a1 |
144.5-a |
$2$ |
$5$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
144.5 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{10} \) |
$1.27630$ |
$(-a-1), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 5 \) |
$1$ |
$2.295286137$ |
2.783443290 |
\( -\frac{13549359104}{243} \) |
\( \bigl[0\) , \( a + 1\) , \( a + 1\) , \( -1936 a - 3028\) , \( 64390 a + 100545\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1936a-3028\right){x}+64390a+100545$ |
| 576.6-b1 |
576.6-b |
$2$ |
$5$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
576.6 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{10} \) |
$1.80496$ |
$(-a-1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 1 \) |
$3.268387907$ |
$3.246024785$ |
5.146250968 |
\( -\frac{13549359104}{243} \) |
\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( 248 a - 644\) , \( -3320 a + 8485\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(248a-644\right){x}-3320a+8485$ |
| 576.6-q1 |
576.6-q |
$2$ |
$5$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
576.6 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{10} \) |
$1.80496$ |
$(-a-1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 5 \) |
$0.033617495$ |
$18.42947588$ |
1.502636295 |
\( -\frac{13549359104}{243} \) |
\( \bigl[0\) , \( 1\) , \( a + 1\) , \( -149 a - 248\) , \( 1420 a + 2236\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-149a-248\right){x}+1420a+2236$ |
| 576.7-b1 |
576.7-b |
$2$ |
$5$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
576.7 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{10} \) |
$1.80496$ |
$(-a+2), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 1 \) |
$3.268387907$ |
$3.246024785$ |
5.146250968 |
\( -\frac{13549359104}{243} \) |
\( \bigl[0\) , \( -a\) , \( a\) , \( -248 a - 396\) , \( 3319 a + 5166\bigr] \) |
${y}^2+a{y}={x}^{3}-a{x}^{2}+\left(-248a-396\right){x}+3319a+5166$ |
| 576.7-q1 |
576.7-q |
$2$ |
$5$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
576.7 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{10} \) |
$1.80496$ |
$(-a+2), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 5 \) |
$0.033617495$ |
$18.42947588$ |
1.502636295 |
\( -\frac{13549359104}{243} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( 149 a - 397\) , \( -1421 a + 3657\bigr] \) |
${y}^2+a{y}={x}^{3}+{x}^{2}+\left(149a-397\right){x}-1421a+3657$ |
*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.
