| 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-a3 |
9.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{2} \) |
$0.43777$ |
$(3)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$63.34616712$ |
0.223962521 |
\( \frac{85184}{3} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -2 a - 3\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-2a-3\right){x}$ |
| 81.1-a3 |
81.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
81.1 |
\( 3^{4} \) |
\( 3^{14} \) |
$0.75824$ |
$(3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$7.969844927$ |
1.408882848 |
\( \frac{85184}{3} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( -17 a - 24\) , \( -52 a - 75\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-17a-24\right){x}-52a-75$ |
| 144.1-a3 |
144.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{2} \) |
$0.87554$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$11.95476739$ |
1.056662136 |
\( \frac{85184}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -8 a - 10\) , \( -14 a - 20\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-8a-10\right){x}-14a-20$ |
| 441.2-a3 |
441.2-a |
$4$ |
$10$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
441.2 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{2} \cdot 7^{6} \) |
$1.15823$ |
$(-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$14.70945947$ |
2.600289635 |
\( \frac{85184}{3} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -6 a - 11\) , \( 9 a + 11\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-6a-11\right){x}+9a+11$ |
| 441.3-a3 |
441.3-a |
$4$ |
$10$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
441.3 |
\( 3^{2} \cdot 7^{2} \) |
\( 3^{2} \cdot 7^{6} \) |
$1.15823$ |
$(2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$14.70945947$ |
2.600289635 |
\( \frac{85184}{3} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 5 a - 11\) , \( -10 a + 11\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(5a-11\right){x}-10a+11$ |
| 1296.1-c3 |
1296.1-c |
$4$ |
$10$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1296.1 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{14} \) |
$1.51647$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$10.55769452$ |
1.866354347 |
\( \frac{85184}{3} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -66 a - 99\) , \( 350 a + 500\bigr] \) |
${y}^2={x}^{3}+\left(-66a-99\right){x}+350a+500$ |
| 2304.1-d3 |
2304.1-d |
$4$ |
$10$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{2} \) |
$1.75107$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$19.45878584$ |
1.719929928 |
\( \frac{85184}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -3\) , \( -3 a\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}-3{x}-3a$ |
| 2304.1-p3 |
2304.1-p |
$4$ |
$10$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{2} \) |
$1.75107$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$19.45878584$ |
1.719929928 |
\( \frac{85184}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -3\) , \( 3 a\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}-3{x}+3a$ |
| 2601.2-a3 |
2601.2-a |
$4$ |
$10$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2601.2 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{2} \cdot 17^{6} \) |
$1.80496$ |
$(3a-1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2 \) |
$0.761474144$ |
$5.798913962$ |
1.561193855 |
\( \frac{85184}{3} \) |
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 6 a - 16\) , \( 10 a - 34\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6a-16\right){x}+10a-34$ |
| 2601.3-a3 |
2601.3-a |
$4$ |
$10$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2601.3 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{2} \cdot 17^{6} \) |
$1.80496$ |
$(-3a-1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2 \) |
$0.761474144$ |
$5.798913962$ |
1.561193855 |
\( \frac{85184}{3} \) |
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -7 a - 16\) , \( -10 a - 34\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-7a-16\right){x}-10a-34$ |
| 3969.2-e3 |
3969.2-e |
$4$ |
$10$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
3969.2 |
\( 3^{4} \cdot 7^{2} \) |
\( 3^{14} \cdot 7^{6} \) |
$2.00611$ |
$(-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{3} \) |
$0.253950066$ |
$4.903153158$ |
1.760916598 |
\( \frac{85184}{3} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( -50 a - 90\) , \( -306 a - 408\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-50a-90\right){x}-306a-408$ |
| 3969.3-e3 |
3969.3-e |
$4$ |
$10$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
3969.3 |
\( 3^{4} \cdot 7^{2} \) |
\( 3^{14} \cdot 7^{6} \) |
$2.00611$ |
$(2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{3} \) |
$0.253950066$ |
$4.903153158$ |
1.760916598 |
\( \frac{85184}{3} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( 49 a - 90\) , \( 306 a - 408\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(49a-90\right){x}+306a-408$ |
| 4761.2-b3 |
4761.2-b |
$4$ |
$10$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
4761.2 |
\( 3^{2} \cdot 23^{2} \) |
\( 3^{2} \cdot 23^{6} \) |
$2.09946$ |
$(-a+5), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$1.081893922$ |
$8.114874657$ |
6.207997012 |
\( \frac{85184}{3} \) |
\( \bigl[a\) , \( a\) , \( a + 1\) , \( 9 a - 25\) , \( -43 a + 37\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(9a-25\right){x}-43a+37$ |
| 4761.3-b3 |
4761.3-b |
$4$ |
$10$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
4761.3 |
\( 3^{2} \cdot 23^{2} \) |
\( 3^{2} \cdot 23^{6} \) |
$2.09946$ |
$(-a-5), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$1.081893922$ |
$8.114874657$ |
6.207997012 |
\( \frac{85184}{3} \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -10 a - 25\) , \( 42 a + 37\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-10a-25\right){x}+42a+37$ |
*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.
