| 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 |
| 18.1-a3 |
18.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( - 2^{8} \cdot 3^{2} \) |
$0.75889$ |
$(-a+2), (3)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$26.89023731$ |
0.815230064 |
\( \frac{1095125}{768} a + \frac{2055079}{768} \) |
\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -2 a\) , \( 1\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}-2a{x}+1$ |
| 144.4-d3 |
144.4-d |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
144.4 |
\( 2^{4} \cdot 3^{2} \) |
\( - 2^{20} \cdot 3^{2} \) |
$1.27630$ |
$(-a+2), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.458834123$ |
$10.04123052$ |
2.234848983 |
\( \frac{1095125}{768} a + \frac{2055079}{768} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -6 a - 8\) , \( 5 a + 8\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-6a-8\right){x}+5a+8$ |
| 162.1-a3 |
162.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
162.1 |
\( 2 \cdot 3^{4} \) |
\( - 2^{8} \cdot 3^{14} \) |
$1.31444$ |
$(-a+2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.878712504$ |
1.183261586 |
\( \frac{1095125}{768} a + \frac{2055079}{768} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -9 a - 12\) , \( -14 a - 24\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-9a-12\right){x}-14a-24$ |
| 288.3-c3 |
288.3-c |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
288.3 |
\( 2^{5} \cdot 3^{2} \) |
\( - 2^{20} \cdot 3^{2} \) |
$1.51779$ |
$(-a+2), (-a-1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.370056505$ |
$9.798829194$ |
1.758926798 |
\( \frac{1095125}{768} a + \frac{2055079}{768} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( a + 3\) , \( -5 a - 7\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a+3\right){x}-5a-7$ |
| 576.7-h3 |
576.7-h |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
576.7 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{26} \cdot 3^{2} \) |
$1.80496$ |
$(-a+2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.928818571$ |
1.680485342 |
\( \frac{1095125}{768} a + \frac{2055079}{768} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -103 a + 264\) , \( -1446 a + 3704\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-103a+264\right){x}-1446a+3704$ |
| 576.7-k3 |
576.7-k |
$6$ |
$8$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
576.7 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{26} \cdot 3^{2} \) |
$1.80496$ |
$(-a+2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.174656042$ |
1.255038437 |
\( \frac{1095125}{768} a + \frac{2055079}{768} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -3 a + 3\) , \( -15\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-3a+3\right){x}-15$ |
*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.
