| 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 |
| 17.1-a1 |
17.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$0.51321$ |
$(-3a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$22.23161552$ |
0.436670169 |
\( -\frac{94464}{289} a + \frac{58688}{289} \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -2 a + 1\) , \( -a\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a+1\right){x}-a$ |
| 272.1-c1 |
272.1-c |
$4$ |
$6$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
272.1 |
\( 2^{4} \cdot 17 \) |
\( 2^{12} \cdot 17^{2} \) |
$1.02642$ |
$(a), (-3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$6.722275873$ |
1.188341713 |
\( -\frac{94464}{289} a + \frac{58688}{289} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -2 a + 3\) , \( -3 a + 4\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-2a+3\right){x}-3a+4$ |
| 289.3-a1 |
289.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
289.3 |
\( 17^{2} \) |
\( 17^{8} \) |
$1.04210$ |
$(-3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.260782761$ |
1.152860801 |
\( -\frac{94464}{289} a + \frac{58688}{289} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( -8 a - 8\) , \( -38 a - 53\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-8a-8\right){x}-38a-53$ |
| 833.3-a1 |
833.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
833.3 |
\( 7^{2} \cdot 17 \) |
\( 7^{6} \cdot 17^{2} \) |
$1.35783$ |
$(-2a+1), (-3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.229438374$ |
$10.78323036$ |
1.749443587 |
\( -\frac{94464}{289} a + \frac{58688}{289} \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( -6 a - 7\) , \( 18 a + 25\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-6a-7\right){x}+18a+25$ |
| 833.5-a1 |
833.5-a |
$4$ |
$6$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
833.5 |
\( 7^{2} \cdot 17 \) |
\( 7^{6} \cdot 17^{2} \) |
$1.35783$ |
$(2a+1), (-3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.959774245$ |
1.399991610 |
\( -\frac{94464}{289} a + \frac{58688}{289} \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( -3 a + 1\) , \( a - 6\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-3a+1\right){x}+a-6$ |
| 1377.1-a1 |
1377.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1377.1 |
\( 3^{4} \cdot 17 \) |
\( 3^{12} \cdot 17^{2} \) |
$1.53963$ |
$(-3a-1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$0.307842315$ |
$4.481517249$ |
1.951049946 |
\( -\frac{94464}{289} a + \frac{58688}{289} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( -5 a + 5\) , \( -10 a + 11\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-5a+5\right){x}-10a+11$ |
| 4352.1-b1 |
4352.1-b |
$4$ |
$6$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
4352.1 |
\( 2^{8} \cdot 17 \) |
\( 2^{12} \cdot 17^{2} \) |
$2.05284$ |
$(a), (-3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$14.26487294$ |
2.521697097 |
\( -\frac{94464}{289} a + \frac{58688}{289} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -2 a\) , \( 2 a + 2\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}-2a{x}+2a+2$ |
| 4352.1-v1 |
4352.1-v |
$4$ |
$6$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
4352.1 |
\( 2^{8} \cdot 17 \) |
\( 2^{12} \cdot 17^{2} \) |
$2.05284$ |
$(a), (-3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$5.238288951$ |
0.926007409 |
\( -\frac{94464}{289} a + \frac{58688}{289} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -2 a\) , \( -2 a - 2\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}-2a{x}-2a-2$ |
| 4624.3-j1 |
4624.3-j |
$4$ |
$6$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
4624.3 |
\( 2^{4} \cdot 17^{2} \) |
\( 2^{12} \cdot 17^{8} \) |
$2.08419$ |
$(a), (-3a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.695979383$ |
0.953172651 |
\( -\frac{94464}{289} a + \frac{58688}{289} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -32 a - 34\) , \( 270 a + 360\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-32a-34\right){x}+270a+360$ |
| 4913.2-a1 |
4913.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
4913.2 |
\( 17^{3} \) |
\( 17^{8} \) |
$2.11602$ |
$(-3a-1), (3a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.492200209$ |
$3.260782761$ |
2.269753309 |
\( -\frac{94464}{289} a + \frac{58688}{289} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -5 a - 1\) , \( -10 a - 5\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-5a-1\right){x}-10a-5$ |
*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.
