| 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 |
| 44217.7-a1 |
44217.7-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
44217.7 |
\( 3^{2} \cdot 17^{3} \) |
\( 3^{16} \cdot 17^{10} \) |
$3.66506$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.107477719$ |
0.303992898 |
\( -\frac{372082589114986904}{2610969633} a - \frac{181318779827784209}{2610969633} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 2191 a - 26002\) , \( -203191 a + 1594414\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(2191a-26002\right){x}-203191a+1594414$ |
| 44217.7-a2 |
44217.7-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
44217.7 |
\( 3^{2} \cdot 17^{3} \) |
\( 3^{8} \cdot 17^{14} \) |
$3.66506$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.214955439$ |
0.303992898 |
\( \frac{147770521717808}{17596287801} a - \frac{136210703475223}{17596287801} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 151 a - 1607\) , \( -2693 a + 25042\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(151a-1607\right){x}-2693a+25042$ |
| 44217.7-a3 |
44217.7-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
44217.7 |
\( 3^{2} \cdot 17^{3} \) |
\( 3^{4} \cdot 17^{19} \) |
$3.66506$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.107477719$ |
0.303992898 |
\( \frac{1695948356939509768}{15730800405203547} a - \frac{7330062339265374821}{15730800405203547} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -1889 a - 332\) , \( -61139 a + 75226\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-1889a-332\right){x}-61139a+75226$ |
| 44217.7-a4 |
44217.7-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
44217.7 |
\( 3^{2} \cdot 17^{3} \) |
\( 3^{4} \cdot 17^{13} \) |
$3.66506$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.429910879$ |
0.303992898 |
\( -\frac{3780522976}{2255067} a + \frac{417620747}{2255067} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 151 a - 162\) , \( 1353 a + 188\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(151a-162\right){x}+1353a+188$ |
| 44217.7-b1 |
44217.7-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
44217.7 |
\( 3^{2} \cdot 17^{3} \) |
\( 3^{16} \cdot 17^{10} \) |
$3.66506$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \cdot 3^{2} \) |
$1$ |
$0.107477719$ |
2.735936085 |
\( \frac{372082589114986904}{2610969633} a - \frac{181318779827784209}{2610969633} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( 16 a + 26186\) , \( -1153284 a + 4369\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(16a+26186\right){x}-1153284a+4369$ |
| 44217.7-b2 |
44217.7-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
44217.7 |
\( 3^{2} \cdot 17^{3} \) |
\( 3^{8} \cdot 17^{14} \) |
$3.66506$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$1$ |
$0.214955439$ |
2.735936085 |
\( -\frac{147770521717808}{17596287801} a - \frac{136210703475223}{17596287801} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( 16 a + 1621\) , \( -18381 a - 544\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(16a+1621\right){x}-18381a-544$ |
| 44217.7-b3 |
44217.7-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
44217.7 |
\( 3^{2} \cdot 17^{3} \) |
\( 3^{4} \cdot 17^{19} \) |
$3.66506$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$0.107477719$ |
2.735936085 |
\( -\frac{1695948356939509768}{15730800405203547} a - \frac{7330062339265374821}{15730800405203547} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( -1904 a + 16\) , \( -63222 a + 70787\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-1904a+16\right){x}-63222a+70787$ |
| 44217.7-b4 |
44217.7-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
44217.7 |
\( 3^{2} \cdot 17^{3} \) |
\( 3^{4} \cdot 17^{13} \) |
$3.66506$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.429910879$ |
2.735936085 |
\( \frac{3780522976}{2255067} a + \frac{417620747}{2255067} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( 136 a + 186\) , \( 60 a - 1825\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(136a+186\right){x}+60a-1825$ |
| 44217.7-c1 |
44217.7-c |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
44217.7 |
\( 3^{2} \cdot 17^{3} \) |
\( 3^{2} \cdot 17^{12} \) |
$3.66506$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$1.281220041$ |
$0.407318629$ |
4.428169593 |
\( -\frac{23100424192}{14739} \) |
\( \bigl[0\) , \( -a\) , \( a + 1\) , \( -712 a - 60\) , \( -6669 a + 7446\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-712a-60\right){x}-6669a+7446$ |
| 44217.7-c2 |
44217.7-c |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
44217.7 |
\( 3^{2} \cdot 17^{3} \) |
\( 3^{6} \cdot 17^{8} \) |
$3.66506$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$0.427073347$ |
$1.221955888$ |
4.428169593 |
\( \frac{32768}{459} \) |
\( \bigl[0\) , \( -a\) , \( a + 1\) , \( 8 a\) , \( -39 a + 51\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+8a{x}-39a+51$ |
| 44217.7-d1 |
44217.7-d |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
44217.7 |
\( 3^{2} \cdot 17^{3} \) |
\( 3^{10} \cdot 17^{10} \) |
$3.66506$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$0.524935341$ |
1.484741359 |
\( \frac{14811123712}{96702579} a + \frac{26737709056}{96702579} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -49 a - 76\) , \( 462 a - 505\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}+\left(-49a-76\right){x}+462a-505$ |
| 44217.7-e1 |
44217.7-e |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
44217.7 |
\( 3^{2} \cdot 17^{3} \) |
\( 3^{10} \cdot 17^{10} \) |
$3.66506$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3^{2} \) |
$1.186590409$ |
$0.524935341$ |
15.85601871 |
\( -\frac{14811123712}{96702579} a + \frac{26737709056}{96702579} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -55 a + 68\) , \( 429 a - 505\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+\left(-55a+68\right){x}+429a-505$ |
*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.
