| 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-a2 |
9.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{2} \) |
$0.63815$ |
$(3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$15.98892188$ |
0.969470791 |
\( -\frac{31564213125250}{3} a + \frac{80853398915125}{3} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 32 a - 79\) , \( -131 a + 330\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(32a-79\right){x}-131a+330$ |
| 81.1-c2 |
81.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
81.1 |
\( 3^{4} \) |
\( - 3^{14} \) |
$1.10531$ |
$(3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.707102506$ |
0.414033173 |
\( -\frac{31564213125250}{3} a + \frac{80853398915125}{3} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 285 a - 725\) , \( 3676 a - 9366\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(285a-725\right){x}+3676a-9366$ |
| 144.4-c2 |
144.4-c |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
144.4 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{12} \cdot 3^{2} \) |
$1.27630$ |
$(-a+2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$1.599650214$ |
0.775944329 |
\( -\frac{31564213125250}{3} a + \frac{80853398915125}{3} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 80 a - 192\) , \( 523 a - 1360\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(80a-192\right){x}+523a-1360$ |
| 144.5-c2 |
144.5-c |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
144.5 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{12} \cdot 3^{2} \) |
$1.27630$ |
$(-a-1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$12.79720171$ |
0.775944329 |
\( -\frac{31564213125250}{3} a + \frac{80853398915125}{3} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 206 a - 531\) , \( -2387 a + 6120\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(206a-531\right){x}-2387a+6120$ |
| 576.6-e2 |
576.6-e |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
576.6 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{18} \cdot 3^{2} \) |
$1.80496$ |
$(-a-1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.913942083$ |
$1.810655637$ |
3.437603564 |
\( -\frac{31564213125250}{3} a + \frac{80853398915125}{3} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 71 a - 156\) , \( 446 a - 779\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(71a-156\right){x}+446a-779$ |
| 576.6-n2 |
576.6-n |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
576.6 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{18} \cdot 3^{2} \) |
$1.80496$ |
$(-a-1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.356632445$ |
$1.131123514$ |
1.841701975 |
\( -\frac{31564213125250}{3} a + \frac{80853398915125}{3} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 294 a + 455\) , \( -43002 a - 67154\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(294a+455\right){x}-43002a-67154$ |
| 576.7-e2 |
576.7-e |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
576.7 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{18} \cdot 3^{2} \) |
$1.80496$ |
$(-a+2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.913942083$ |
$1.810655637$ |
3.437603564 |
\( -\frac{31564213125250}{3} a + \frac{80853398915125}{3} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 974 a - 2497\) , \( 24826 a - 63589\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(974a-2497\right){x}+24826a-63589$ |
| 576.7-n2 |
576.7-n |
$8$ |
$16$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
576.7 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{18} \cdot 3^{2} \) |
$1.80496$ |
$(-a+2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.839158111$ |
$9.048988114$ |
1.841701975 |
\( -\frac{31564213125250}{3} a + \frac{80853398915125}{3} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 34 a - 9\) , \( 701 a + 1285\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(34a-9\right){x}+701a+1285$ |
*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.
