| 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 |
| 64.4-a1 |
64.4-a |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{13} \) |
$1.04210$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$7.156385278$ |
0.867839188 |
\( \frac{217}{16} a - \frac{139}{4} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 0\) , \( -2 a - 4\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}-2a-4$ |
| 64.4-a2 |
64.4-a |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{10} \) |
$1.04210$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$7.156385278$ |
0.867839188 |
\( -\frac{23841914775}{2} a + 30536164178 \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 171 a - 436\) , \( 1835 a - 4700\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(171a-436\right){x}+1835a-4700$ |
| 64.4-a3 |
64.4-a |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{8} \) |
$1.04210$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$14.31277055$ |
0.867839188 |
\( -\frac{159495}{4} a + 160181 \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 11 a - 26\) , \( 33 a - 84\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(11a-26\right){x}+33a-84$ |
| 64.4-a4 |
64.4-a |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{13} \) |
$1.04210$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$7.156385278$ |
0.867839188 |
\( \frac{1592342311}{2} a + 1243265046 \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 16 a - 41\) , \( 4 a - 13\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(16a-41\right){x}+4a-13$ |
| 64.4-b1 |
64.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{13} \) |
$1.04210$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$14.01972920$ |
1.700141892 |
\( \frac{217}{16} a - \frac{139}{4} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -3\) , \( -3 a + 6\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}-3{x}-3a+6$ |
| 64.4-b2 |
64.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{10} \) |
$1.04210$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$28.03945840$ |
1.700141892 |
\( -\frac{23841914775}{2} a + 30536164178 \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -3 a - 12\) , \( 3 a + 8\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a-12\right){x}+3a+8$ |
| 64.4-b3 |
64.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{8} \) |
$1.04210$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$28.03945840$ |
1.700141892 |
\( -\frac{159495}{4} a + 160181 \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -3 a - 2\) , \( -3 a - 4\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a-2\right){x}-3a-4$ |
| 64.4-b4 |
64.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{17}) \) |
$2$ |
$[2, 0]$ |
64.4 |
\( 2^{6} \) |
\( 2^{13} \) |
$1.04210$ |
$(-a+2), (-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.009864600$ |
1.700141892 |
\( \frac{1592342311}{2} a + 1243265046 \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -38 a - 57\) , \( -180 a - 281\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-38a-57\right){x}-180a-281$ |
*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.
