| 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 |
| 41616.6-a1 |
41616.6-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{4} \cdot 3^{8} \cdot 17^{8} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$0.659581703$ |
1.865578780 |
\( -\frac{143805376}{7803} a - \frac{629322032}{23409} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 113 a - 134\) , \( 830 a - 317\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(113a-134\right){x}+830a-317$ |
| 41616.6-a2 |
41616.6-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{8} \cdot 3^{10} \cdot 17^{10} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \) |
$1$ |
$0.329790851$ |
1.865578780 |
\( -\frac{129263405128}{547981281} a - \frac{3842395588}{547981281} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 163 a + 111\) , \( 1389 a - 3040\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(163a+111\right){x}+1389a-3040$ |
| 41616.6-a3 |
41616.6-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{8} \cdot 3^{10} \cdot 17^{7} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.659581703$ |
1.865578780 |
\( \frac{85372928}{111537} a + \frac{75126784}{111537} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 12 a - 95\) , \( -114 a - 336\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(12a-95\right){x}-114a-336$ |
| 41616.6-a4 |
41616.6-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{10} \cdot 3^{5} \cdot 17^{14} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.164895425$ |
1.865578780 |
\( \frac{2645795907052078}{565036352721} a + \frac{2516554590655786}{565036352721} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -1667 a + 681\) , \( 7881 a - 42670\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-1667a+681\right){x}+7881a-42670$ |
| 41616.6-a5 |
41616.6-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{10} \cdot 3^{17} \cdot 17^{8} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.164895425$ |
1.865578780 |
\( \frac{4578846951098354}{12440502369} a + \frac{1040330832518918}{12440502369} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 2793 a + 3461\) , \( 30273 a - 139642\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(2793a+3461\right){x}+30273a-139642$ |
| 41616.6-a6 |
41616.6-a |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 17^{7} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$1$ |
$0.329790851$ |
1.865578780 |
\( \frac{155804663816}{153} a + \frac{4264024316}{51} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 1823 a - 2159\) , \( 51599 a - 19712\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(1823a-2159\right){x}+51599a-19712$ |
| 41616.6-b1 |
41616.6-b |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{12} \cdot 3^{11} \cdot 17^{2} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.453574129$ |
$1.591189954$ |
4.082679550 |
\( -\frac{32269}{729} a - \frac{34727}{729} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -4 a + 4\) , \( -8 a + 32\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-4a+4\right){x}-8a+32$ |
| 41616.6-c1 |
41616.6-c |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{12} \cdot 3^{11} \cdot 17^{8} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 3 \cdot 5 \) |
$0.187154383$ |
$0.385920250$ |
6.128635888 |
\( -\frac{32269}{729} a - \frac{34727}{729} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 42 a + 101\) , \( 1533 a - 931\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(42a+101\right){x}+1533a-931$ |
| 41616.6-d1 |
41616.6-d |
$4$ |
$10$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{17} \cdot 3^{32} \cdot 17^{9} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$25$ |
\( 2^{4} \) |
$1$ |
$0.032781840$ |
2.318026149 |
\( -\frac{811409154866127821}{1647129056757192} a - \frac{79261954805628389}{411782264189298} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 23093 a - 2242\) , \( -1094982 a - 3495813\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(23093a-2242\right){x}-1094982a-3495813$ |
| 41616.6-d2 |
41616.6-d |
$4$ |
$10$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{14} \cdot 3^{8} \cdot 17^{9} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.327818401$ |
2.318026149 |
\( \frac{507662}{243} a + \frac{2905757}{486} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -347 a - 342\) , \( -3226 a - 317\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-347a-342\right){x}-3226a-317$ |
| 41616.6-d3 |
41616.6-d |
$4$ |
$10$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{13} \cdot 3^{16} \cdot 17^{9} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \cdot 5 \) |
$1$ |
$0.163909200$ |
2.318026149 |
\( -\frac{362392621}{118098} a + \frac{474522278}{59049} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -1247 a - 1862\) , \( 29870 a + 21515\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1247a-1862\right){x}+29870a+21515$ |
| 41616.6-d4 |
41616.6-d |
$4$ |
$10$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{22} \cdot 3^{16} \cdot 17^{9} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$25$ |
\( 2^{3} \) |
$1$ |
$0.065563680$ |
2.318026149 |
\( \frac{105956215006891}{114791256} a + \frac{9859152651013}{459165024} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 26693 a + 3838\) , \( -1206310 a - 2275877\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(26693a+3838\right){x}-1206310a-2275877$ |
| 41616.6-e1 |
41616.6-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{4} \cdot 3^{6} \cdot 17^{8} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$0.951404560$ |
2.690978464 |
\( -\frac{6022432}{23409} a + \frac{36070448}{23409} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 10 a + 50\) , \( -64 a - 53\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(10a+50\right){x}-64a-53$ |
| 41616.6-e2 |
41616.6-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 17^{7} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.951404560$ |
2.690978464 |
\( \frac{413696}{1377} a + \frac{2547712}{1377} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -14 a - 50\) , \( 62 a + 23\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-14a-50\right){x}+62a+23$ |
| 41616.6-e3 |
41616.6-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{8} \cdot 3^{3} \cdot 17^{10} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.475702280$ |
2.690978464 |
\( \frac{55772510924}{751689} a + \frac{25628760668}{751689} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 175 a + 425\) , \( 1832 a - 3074\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(175a+425\right){x}+1832a-3074$ |
| 41616.6-e4 |
41616.6-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{8} \cdot 3^{9} \cdot 17^{7} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.475702280$ |
2.690978464 |
\( -\frac{54042238124}{111537} a + \frac{8383142164}{111537} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 45 a + 655\) , \( -4776 a + 614\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(45a+655\right){x}-4776a+614$ |
| 41616.6-f1 |
41616.6-f |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{28} \cdot 3^{9} \cdot 17^{2} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$0.761387392$ |
2.153528752 |
\( \frac{3805069}{559872} a - \frac{2875943}{559872} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -10 a + 3\) , \( -9 a + 293\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-10a+3\right){x}-9a+293$ |
| 41616.6-g1 |
41616.6-g |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{10} \cdot 3^{16} \cdot 17^{6} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$0.518025393$ |
$0.440850580$ |
5.167463847 |
\( \frac{207646}{6561} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 48 a + 5\) , \( -855 a + 1013\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(48a+5\right){x}-855a+1013$ |
| 41616.6-g2 |
41616.6-g |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 17^{6} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$4.144203148$ |
$1.763402322$ |
5.167463847 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 8 a\) , \( -10 a + 17\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+8a{x}-10a+17$ |
| 41616.6-g3 |
41616.6-g |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 17^{6} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$2.072101574$ |
$1.763402322$ |
5.167463847 |
\( \frac{35152}{9} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -12 a\) , \( 19 a - 22\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}-12a{x}+19a-22$ |
| 41616.6-g4 |
41616.6-g |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 17^{6} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1.036050787$ |
$0.881701161$ |
5.167463847 |
\( \frac{1556068}{81} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -72 a - 5\) , \( -171 a + 203\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-72a-5\right){x}-171a+203$ |
| 41616.6-g5 |
41616.6-g |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{11} \cdot 3^{20} \cdot 17^{6} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{8} \) |
$0.259012696$ |
$0.220425290$ |
5.167463847 |
\( -\frac{2327042746553}{43046721} a + \frac{2081263802600}{43046721} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 1078 a - 1595\) , \( -25633 a + 17685\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(1078a-1595\right){x}-25633a+17685$ |
| 41616.6-g6 |
41616.6-g |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{11} \cdot 3^{20} \cdot 17^{6} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1.036050787$ |
$0.220425290$ |
5.167463847 |
\( \frac{2327042746553}{43046721} a + \frac{2081263802600}{43046721} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 938 a + 1765\) , \( -16813 a + 32581\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(938a+1765\right){x}-16813a+32581$ |
| 41616.6-g7 |
41616.6-g |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 17^{6} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$4.144203148$ |
$0.881701161$ |
5.167463847 |
\( \frac{28756228}{3} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -192 a - 15\) , \( 1045 a - 1237\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-192a-15\right){x}+1045a-1237$ |
| 41616.6-g8 |
41616.6-g |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{10} \cdot 3^{4} \cdot 17^{6} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.518025393$ |
$0.440850580$ |
5.167463847 |
\( \frac{3065617154}{9} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -1152 a - 95\) , \( -13167 a + 15593\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1152a-95\right){x}-13167a+15593$ |
| 41616.6-h1 |
41616.6-h |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 17^{7} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.539936468$ |
3.054341906 |
\( -\frac{2360418304}{1377} a - \frac{2892359680}{1377} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -160 a - 591\) , \( 2206 a + 5038\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-160a-591\right){x}+2206a+5038$ |
| 41616.6-h2 |
41616.6-h |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{10} \cdot 3^{18} \cdot 17^{8} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{9} \) |
$1$ |
$0.134984117$ |
3.054341906 |
\( \frac{5885451972543220}{12440502369} a - \frac{19099058671357966}{12440502369} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 5845 a + 4196\) , \( -20646 a - 343269\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(5845a+4196\right){x}-20646a-343269$ |
| 41616.6-h3 |
41616.6-h |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{10} \cdot 3^{6} \cdot 17^{14} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1$ |
$0.134984117$ |
3.054341906 |
\( -\frac{14877988411966900}{565036352721} a - \frac{9880475817788162}{565036352721} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 1245 a + 4776\) , \( -87210 a + 68211\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(1245a+4776\right){x}-87210a+68211$ |
| 41616.6-h4 |
41616.6-h |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{11} \cdot 3^{33} \cdot 17^{7} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{8} \) |
$1$ |
$0.067492058$ |
3.054341906 |
\( -\frac{25029803989100500051}{31501343210481297} a + \frac{13780334126509226890}{31501343210481297} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 6155 a + 2536\) , \( 68942 a - 383681\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(6155a+2536\right){x}+68942a-383681$ |
| 41616.6-h5 |
41616.6-h |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{8} \cdot 3^{18} \cdot 17^{7} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{8} \) |
$1$ |
$0.269968234$ |
3.054341906 |
\( \frac{15399836042224}{731794257} a + \frac{536897734540}{731794257} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -695 a - 684\) , \( 11342 a + 1669\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-695a-684\right){x}+11342a+1669$ |
| 41616.6-h6 |
41616.6-h |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 17^{10} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$1$ |
$0.269968234$ |
3.054341906 |
\( \frac{431439408400}{547981281} a + \frac{562795252868}{547981281} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 345 a + 366\) , \( -1800 a - 4869\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(345a+366\right){x}-1800a-4869$ |
| 41616.6-h7 |
41616.6-h |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 17^{8} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.539936468$ |
3.054341906 |
\( -\frac{2043733120}{1896129} a + \frac{2899292624}{1896129} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -55 a - 149\) , \( -121 a - 659\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-55a-149\right){x}-121a-659$ |
| 41616.6-h8 |
41616.6-h |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{11} \cdot 3^{9} \cdot 17^{7} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{6} \) |
$1$ |
$0.067492058$ |
3.054341906 |
\( -\frac{162097126731251789}{111537} a + \frac{213213879499887110}{111537} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 93535 a + 67136\) , \( -1272378 a - 21929817\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(93535a+67136\right){x}-1272378a-21929817$ |
| 41616.6-i1 |
41616.6-i |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{28} \cdot 3^{9} \cdot 17^{8} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$0.184663567$ |
3.656152093 |
\( \frac{3805069}{559872} a - \frac{2875943}{559872} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 12 a + 267\) , \( 12036 a - 12530\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(12a+267\right){x}+12036a-12530$ |
| 41616.6-j1 |
41616.6-j |
$4$ |
$10$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{17} \cdot 3^{32} \cdot 17^{3} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{5} \cdot 3 \cdot 5 \) |
$0.331311827$ |
$0.135162989$ |
7.599604181 |
\( -\frac{811409154866127821}{1647129056757192} a - \frac{79261954805628389}{411782264189298} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 173 a + 1910\) , \( 37068 a + 15081\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(173a+1910\right){x}+37068a+15081$ |
| 41616.6-j2 |
41616.6-j |
$4$ |
$10$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{14} \cdot 3^{8} \cdot 17^{3} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \cdot 3 \cdot 5 \) |
$0.132524730$ |
$1.351629896$ |
7.599604181 |
\( \frac{507662}{243} a + \frac{2905757}{486} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 13 a - 30\) , \( 32 a - 47\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(13a-30\right){x}+32a-47$ |
| 41616.6-j3 |
41616.6-j |
$4$ |
$10$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{13} \cdot 3^{16} \cdot 17^{3} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{5} \cdot 3 \cdot 5 \) |
$0.066262365$ |
$0.675814948$ |
7.599604181 |
\( -\frac{362392621}{118098} a + \frac{474522278}{59049} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 73 a - 110\) , \( -440 a + 265\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(73a-110\right){x}-440a+265$ |
| 41616.6-j4 |
41616.6-j |
$4$ |
$10$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{22} \cdot 3^{16} \cdot 17^{3} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \cdot 3 \cdot 5 \) |
$0.662623654$ |
$0.270325979$ |
7.599604181 |
\( \frac{105956215006891}{114791256} a + \frac{9859152651013}{459165024} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -67 a + 2230\) , \( 28652 a + 2185\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-67a+2230\right){x}+28652a+2185$ |
| 41616.6-k1 |
41616.6-k |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{11} \cdot 3^{4} \cdot 17^{10} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.277261365$ |
4.705281399 |
\( -\frac{2574423778799}{2255067} a - \frac{3766534479388}{2255067} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 1566 a - 615\) , \( 27618 a + 15790\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(1566a-615\right){x}+27618a+15790$ |
| 41616.6-k2 |
41616.6-k |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{11} \cdot 3^{16} \cdot 17^{7} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \cdot 3 \) |
$1$ |
$0.277261365$ |
4.705281399 |
\( -\frac{66005182339}{9034497} a - \frac{182256471836}{9034497} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 546 a + 745\) , \( 3582 a - 13090\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(546a+745\right){x}+3582a-13090$ |
| 41616.6-k3 |
41616.6-k |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{10} \cdot 3^{8} \cdot 17^{8} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \cdot 3 \) |
$1$ |
$0.554522730$ |
4.705281399 |
\( \frac{193668952}{210681} a + \frac{24854222}{210681} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 96 a - 15\) , \( 528 a + 94\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(96a-15\right){x}+528a+94$ |
| 41616.6-k4 |
41616.6-k |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.6 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{8} \cdot 3^{4} \cdot 17^{7} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$1.109045461$ |
4.705281399 |
\( -\frac{933536}{459} a + \frac{346508}{459} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -24 a - 25\) , \( 72 a + 56\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-24a-25\right){x}+72a+56$ |
*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.
