| 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 |
| 23409.8-a1 |
23409.8-a |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
23409.8 |
\( 3^{4} \cdot 17^{2} \) |
\( 3^{6} \cdot 17^{2} \) |
$3.12629$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.069480281$ |
$4.574307975$ |
1.797885198 |
\( -\frac{110592}{17} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -3\) , \( 2\bigr] \) |
${y}^2+{y}={x}^{3}-3{x}+2$ |
| 23409.8-b1 |
23409.8-b |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
23409.8 |
\( 3^{4} \cdot 17^{2} \) |
\( 3^{14} \cdot 17^{5} \) |
$3.12629$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.463200697$ |
$0.930162799$ |
2.437267295 |
\( -\frac{4375968098}{1193859} a - \frac{83257760131}{1193859} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 82 a - 26\) , \( -306 a - 318\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(82a-26\right){x}-306a-318$ |
| 23409.8-b2 |
23409.8-b |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
23409.8 |
\( 3^{4} \cdot 17^{2} \) |
\( 3^{19} \cdot 17^{7} \) |
$3.12629$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.926401395$ |
$0.465081399$ |
2.437267295 |
\( \frac{454229228687227}{1425299311881} a + \frac{679301259838487}{1425299311881} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 67 a - 131\) , \( -105 a - 1206\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(67a-131\right){x}-105a-1206$ |
| 23409.8-c1 |
23409.8-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
23409.8 |
\( 3^{4} \cdot 17^{2} \) |
\( 3^{28} \cdot 17^{4} \) |
$3.12629$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1.255563294$ |
$0.147713997$ |
3.147433083 |
\( -\frac{372082589114986904}{2610969633} a - \frac{181318779827784209}{2610969633} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 9785 a + 827\) , \( 287614 a + 472652\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(9785a+827\right){x}+287614a+472652$ |
| 23409.8-c2 |
23409.8-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
23409.8 |
\( 3^{4} \cdot 17^{2} \) |
\( 3^{20} \cdot 17^{8} \) |
$3.12629$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \cdot 3 \) |
$0.627781647$ |
$0.295427994$ |
3.147433083 |
\( \frac{147770521717808}{17596287801} a - \frac{136210703475223}{17596287801} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 605 a + 62\) , \( 4870 a + 6920\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(605a+62\right){x}+4870a+6920$ |
| 23409.8-c3 |
23409.8-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
23409.8 |
\( 3^{4} \cdot 17^{2} \) |
\( 3^{16} \cdot 17^{13} \) |
$3.12629$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1.255563294$ |
$0.147713997$ |
3.147433083 |
\( \frac{1695948356939509768}{15730800405203547} a - \frac{7330062339265374821}{15730800405203547} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 65 a - 1423\) , \( 118 a + 43424\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(65a-1423\right){x}+118a+43424$ |
| 23409.8-c4 |
23409.8-c |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
23409.8 |
\( 3^{4} \cdot 17^{2} \) |
\( 3^{16} \cdot 17^{7} \) |
$3.12629$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \cdot 3 \) |
$0.313890823$ |
$0.590855988$ |
3.147433083 |
\( -\frac{3780522976}{2255067} a + \frac{417620747}{2255067} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 65 a + 107\) , \( 442 a - 514\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(65a+107\right){x}+442a-514$ |
| 23409.8-d1 |
23409.8-d |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
23409.8 |
\( 3^{4} \cdot 17^{2} \) |
\( 3^{14} \cdot 17^{5} \) |
$3.12629$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.463200697$ |
$0.930162799$ |
2.437267295 |
\( \frac{4375968098}{1193859} a - \frac{83257760131}{1193859} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -82 a - 25\) , \( 281 a - 154\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-82a-25\right){x}+281a-154$ |
| 23409.8-d2 |
23409.8-d |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
23409.8 |
\( 3^{4} \cdot 17^{2} \) |
\( 3^{19} \cdot 17^{7} \) |
$3.12629$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.926401395$ |
$0.465081399$ |
2.437267295 |
\( -\frac{454229228687227}{1425299311881} a + \frac{679301259838487}{1425299311881} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -67 a - 130\) , \( -25 a - 1072\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-67a-130\right){x}-25a-1072$ |
| 23409.8-e1 |
23409.8-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
23409.8 |
\( 3^{4} \cdot 17^{2} \) |
\( 3^{28} \cdot 17^{4} \) |
$3.12629$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1.255563294$ |
$0.147713997$ |
3.147433083 |
\( \frac{372082589114986904}{2610969633} a - \frac{181318779827784209}{2610969633} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -9785 a + 826\) , \( -286787 a + 492222\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-9785a+826\right){x}-286787a+492222$ |
| 23409.8-e2 |
23409.8-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
23409.8 |
\( 3^{4} \cdot 17^{2} \) |
\( 3^{20} \cdot 17^{8} \) |
$3.12629$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \cdot 3 \) |
$0.627781647$ |
$0.295427994$ |
3.147433083 |
\( -\frac{147770521717808}{17596287801} a - \frac{136210703475223}{17596287801} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -605 a + 61\) , \( -4808 a + 8130\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-605a+61\right){x}-4808a+8130$ |
| 23409.8-e3 |
23409.8-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
23409.8 |
\( 3^{4} \cdot 17^{2} \) |
\( 3^{16} \cdot 17^{13} \) |
$3.12629$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1.255563294$ |
$0.147713997$ |
3.147433083 |
\( -\frac{1695948356939509768}{15730800405203547} a - \frac{7330062339265374821}{15730800405203547} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -65 a - 1424\) , \( -1541 a + 43554\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-65a-1424\right){x}-1541a+43554$ |
| 23409.8-e4 |
23409.8-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
23409.8 |
\( 3^{4} \cdot 17^{2} \) |
\( 3^{16} \cdot 17^{7} \) |
$3.12629$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \cdot 3 \) |
$0.313890823$ |
$0.590855988$ |
3.147433083 |
\( \frac{3780522976}{2255067} a + \frac{417620747}{2255067} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -65 a + 106\) , \( -335 a - 384\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-65a+106\right){x}-335a-384$ |
| 23409.8-f1 |
23409.8-f |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
23409.8 |
\( 3^{4} \cdot 17^{2} \) |
\( 3^{18} \cdot 17^{7} \) |
$3.12629$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1$ |
$0.507090095$ |
0.717133690 |
\( -\frac{1875101184}{24137569} a - \frac{11541230784}{24137569} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( 67 a + 75\) , \( 189 a - 1077\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(67a+75\right){x}+189a-1077$ |
| 23409.8-f2 |
23409.8-f |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
23409.8 |
\( 3^{4} \cdot 17^{2} \) |
\( 3^{6} \cdot 17^{7} \) |
$3.12629$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$0$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$1.521270287$ |
0.717133690 |
\( \frac{1875101184}{24137569} a - \frac{11541230784}{24137569} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( -8 a + 9\) , \( 12 a + 34\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-8a+9\right){x}+12a+34$ |
| 23409.8-f3 |
23409.8-f |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
23409.8 |
\( 3^{4} \cdot 17^{2} \) |
\( 3^{6} \cdot 17^{5} \) |
$3.12629$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$0$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$1.521270287$ |
0.717133690 |
\( -\frac{937944576}{4913} a + \frac{5404256064}{4913} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( -38 a + 45\) , \( -21 a - 236\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-38a+45\right){x}-21a-236$ |
| 23409.8-f4 |
23409.8-f |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
23409.8 |
\( 3^{4} \cdot 17^{2} \) |
\( 3^{18} \cdot 17^{5} \) |
$3.12629$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1$ |
$0.507090095$ |
0.717133690 |
\( \frac{937944576}{4913} a + \frac{5404256064}{4913} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( 337 a + 399\) , \( -1242 a + 5565\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(337a+399\right){x}-1242a+5565$ |
| 23409.8-g1 |
23409.8-g |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
23409.8 |
\( 3^{4} \cdot 17^{2} \) |
\( 3^{6} \cdot 17^{7} \) |
$3.12629$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$0$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$1.521270287$ |
0.717133690 |
\( -\frac{1875101184}{24137569} a - \frac{11541230784}{24137569} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( 7 a + 9\) , \( -12 a + 34\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(7a+9\right){x}-12a+34$ |
| 23409.8-g2 |
23409.8-g |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
23409.8 |
\( 3^{4} \cdot 17^{2} \) |
\( 3^{18} \cdot 17^{7} \) |
$3.12629$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1$ |
$0.507090095$ |
0.717133690 |
\( \frac{1875101184}{24137569} a - \frac{11541230784}{24137569} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( -68 a + 75\) , \( -189 a - 1077\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-68a+75\right){x}-189a-1077$ |
| 23409.8-g3 |
23409.8-g |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
23409.8 |
\( 3^{4} \cdot 17^{2} \) |
\( 3^{18} \cdot 17^{5} \) |
$3.12629$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1$ |
$0.507090095$ |
0.717133690 |
\( -\frac{937944576}{4913} a + \frac{5404256064}{4913} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( -338 a + 399\) , \( 1242 a + 5565\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-338a+399\right){x}+1242a+5565$ |
| 23409.8-g4 |
23409.8-g |
$4$ |
$6$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
23409.8 |
\( 3^{4} \cdot 17^{2} \) |
\( 3^{6} \cdot 17^{5} \) |
$3.12629$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$0$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$1.521270287$ |
0.717133690 |
\( \frac{937944576}{4913} a + \frac{5404256064}{4913} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( 37 a + 45\) , \( 21 a - 236\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(37a+45\right){x}+21a-236$ |
| 23409.8-h1 |
23409.8-h |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
23409.8 |
\( 3^{4} \cdot 17^{2} \) |
\( 3^{14} \cdot 17^{6} \) |
$3.12629$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$0.338669215$ |
$0.559805910$ |
4.289910009 |
\( -\frac{23100424192}{14739} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -534\) , \( 4752\bigr] \) |
${y}^2+{y}={x}^{3}-534{x}+4752$ |
| 23409.8-h2 |
23409.8-h |
$2$ |
$3$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
23409.8 |
\( 3^{4} \cdot 17^{2} \) |
\( 3^{18} \cdot 17^{2} \) |
$3.12629$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2^{4} \) |
$0.112889738$ |
$1.679417732$ |
4.289910009 |
\( \frac{32768}{459} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 6\) , \( 27\bigr] \) |
${y}^2+{y}={x}^{3}+6{x}+27$ |
| 23409.8-i1 |
23409.8-i |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
23409.8 |
\( 3^{4} \cdot 17^{2} \) |
\( 3^{12} \cdot 17^{8} \) |
$3.12629$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.247582370$ |
$0.707979566$ |
4.996489067 |
\( -\frac{35937}{83521} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -6\) , \( 377\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-6{x}+377$ |
| 23409.8-i2 |
23409.8-i |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
23409.8 |
\( 3^{4} \cdot 17^{2} \) |
\( 3^{12} \cdot 17^{2} \) |
$3.12629$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.247582370$ |
$2.831918265$ |
4.996489067 |
\( \frac{35937}{17} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -6\) , \( -1\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-6{x}-1$ |
| 23409.8-i3 |
23409.8-i |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
23409.8 |
\( 3^{4} \cdot 17^{2} \) |
\( 3^{12} \cdot 17^{4} \) |
$3.12629$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.623791185$ |
$1.415959132$ |
4.996489067 |
\( \frac{20346417}{289} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -51\) , \( 152\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-51{x}+152$ |
| 23409.8-i4 |
23409.8-i |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
23409.8 |
\( 3^{4} \cdot 17^{2} \) |
\( 3^{12} \cdot 17^{2} \) |
$3.12629$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1.247582370$ |
$0.707979566$ |
4.996489067 |
\( \frac{82483294977}{17} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -816\) , \( 9179\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-816{x}+9179$ |
| 23409.8-j1 |
23409.8-j |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
23409.8 |
\( 3^{4} \cdot 17^{2} \) |
\( 3^{22} \cdot 17^{4} \) |
$3.12629$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$0.721454620$ |
4.081163634 |
\( \frac{14811123712}{96702579} a + \frac{26737709056}{96702579} \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 27 a - 39\) , \( -a - 317\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(27a-39\right){x}-a-317$ |
| 23409.8-k1 |
23409.8-k |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
23409.8 |
\( 3^{4} \cdot 17^{2} \) |
\( 3^{22} \cdot 17^{4} \) |
$3.12629$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$0.721454620$ |
4.081163634 |
\( -\frac{14811123712}{96702579} a + \frac{26737709056}{96702579} \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( -27 a - 39\) , \( -317\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-27a-39\right){x}-317$ |
| 23409.8-l1 |
23409.8-l |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
23409.8 |
\( 3^{4} \cdot 17^{2} \) |
\( 3^{18} \cdot 17^{2} \) |
$3.12629$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2^{2} \) |
$1.159378227$ |
$1.524769325$ |
10.00009845 |
\( -\frac{110592}{17} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -27\) , \( -61\bigr] \) |
${y}^2+{y}={x}^{3}-27{x}-61$ |
*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.
