| 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 |
| 52.1-a1 |
52.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{32} \cdot 13^{4} \) |
$1.93462$ |
$(2,a), (2,a+1), (13,a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$2.930708174$ |
0.727019221 |
\( -\frac{102641119396563}{90731184128} a - \frac{209006099514109}{90731184128} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -5416 a + 24540\) , \( 63920 a - 289630\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-5416a+24540\right){x}+63920a-289630$ |
| 52.1-b1 |
52.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{44} \cdot 13^{4} \) |
$1.93462$ |
$(2,a), (2,a+1), (13,a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \cdot 3 \cdot 29 \) |
$0.022004812$ |
$2.930708174$ |
5.567276826 |
\( \frac{102641119396563}{90731184128} a - \frac{19477951181917}{5670699008} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 212 a - 912\) , \( -3120 a + 14144\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(212a-912\right){x}-3120a+14144$ |
| 52.1-c1 |
52.1-c |
$2$ |
$3$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{30} \cdot 13^{6} \) |
$1.93462$ |
$(2,a), (2,a+1), (13,a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$1.446471516$ |
3.229428790 |
\( -\frac{94024500233}{71991296} a - \frac{13647943289}{4499456} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -86 a + 352\) , \( 24 a - 192\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-86a+352\right){x}+24a-192$ |
| 52.1-c2 |
52.1-c |
$2$ |
$3$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{26} \cdot 13^{2} \) |
$1.93462$ |
$(2,a), (2,a+1), (13,a+6)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$13.01824364$ |
3.229428790 |
\( \frac{5819681}{6656} a - \frac{14984641}{6656} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 9 a - 48\) , \( -22 a + 96\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(9a-48\right){x}-22a+96$ |
| 52.1-d1 |
52.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{14} \cdot 13^{2} \) |
$1.93462$ |
$(2,a), (2,a+1), (13,a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 5 \) |
$0.078047655$ |
$13.01824364$ |
2.520493447 |
\( -\frac{5819681}{6656} a - \frac{286405}{208} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -53 a - 180\) , \( 535 a + 1893\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-53a-180\right){x}+535a+1893$ |
| 52.1-d2 |
52.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{18} \cdot 13^{6} \) |
$1.93462$ |
$(2,a), (2,a+1), (13,a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \cdot 5 \) |
$0.234142965$ |
$1.446471516$ |
2.520493447 |
\( \frac{94024500233}{71991296} a - \frac{312391592857}{71991296} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 362 a + 1285\) , \( -2717 a - 9591\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(362a+1285\right){x}-2717a-9591$ |
| 52.1-e1 |
52.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{22} \cdot 13^{2} \) |
$1.93462$ |
$(2,a), (2,a+1), (13,a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 3^{2} \) |
$0.079975725$ |
$9.192703767$ |
3.282821557 |
\( -\frac{1105705513}{6656} a - \frac{248475817}{416} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -138 a - 488\) , \( 1364 a + 4816\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-138a-488\right){x}+1364a+4816$ |
| 52.1-f1 |
52.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{10} \cdot 13^{2} \) |
$1.93462$ |
$(2,a), (2,a+1), (13,a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$9.192703767$ |
2.280429143 |
\( \frac{1105705513}{6656} a - \frac{5081318585}{6656} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( a - 10\) , \( -3 a + 4\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(a-10\right){x}-3a+4$ |
| 52.1-g1 |
52.1-g |
$3$ |
$9$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{30} \cdot 13^{2} \) |
$1.93462$ |
$(2,a), (2,a+1), (13,a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3^{4} \) |
$1$ |
$0.265819283$ |
5.341273529 |
\( -\frac{10730978619193}{6656} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 834028 a - 3779088\) , \( 834559696 a - 3781497536\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(834028a-3779088\right){x}+834559696a-3781497536$ |
| 52.1-g2 |
52.1-g |
$3$ |
$9$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{18} \cdot 13^{6} \) |
$1.93462$ |
$(2,a), (2,a+1), (13,a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$2.392373550$ |
5.341273529 |
\( -\frac{10218313}{17576} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 8203 a - 37168\) , \( 1639881 a - 7430512\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(8203a-37168\right){x}+1639881a-7430512$ |
| 52.1-g3 |
52.1-g |
$3$ |
$9$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{14} \cdot 13^{2} \) |
$1.93462$ |
$(2,a), (2,a+1), (13,a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$21.53136195$ |
5.341273529 |
\( \frac{12167}{26} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -872 a + 3952\) , \( -48214 a + 218464\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-872a+3952\right){x}-48214a+218464$ |
| 52.1-h1 |
52.1-h |
$2$ |
$7$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{14} \cdot 13^{14} \) |
$1.93462$ |
$(2,a), (2,a+1), (13,a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.6.3 |
$1$ |
\( 2 \cdot 7 \) |
$1.383448027$ |
$0.385597965$ |
1.852673694 |
\( -\frac{1064019559329}{125497034} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 386026 a - 1749144\) , \( 288323272 a - 1306429908\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(386026a-1749144\right){x}+288323272a-1306429908$ |
| 52.1-h2 |
52.1-h |
$2$ |
$7$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{26} \cdot 13^{2} \) |
$1.93462$ |
$(2,a), (2,a+1), (13,a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.6.1 |
$1$ |
\( 2 \) |
$0.197635432$ |
$18.89430030$ |
1.852673694 |
\( -\frac{2146689}{1664} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 4876 a - 22104\) , \( -560288 a + 2538732\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(4876a-22104\right){x}-560288a+2538732$ |
| 52.1-i1 |
52.1-i |
$2$ |
$7$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{2} \cdot 13^{14} \) |
$1.93462$ |
$(2,a), (2,a+1), (13,a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.3 |
$49$ |
\( 2 \) |
$1$ |
$0.385597965$ |
4.687099046 |
\( -\frac{1064019559329}{125497034} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -213\) , \( -1257\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-213{x}-1257$ |
| 52.1-i2 |
52.1-i |
$2$ |
$7$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{14} \cdot 13^{2} \) |
$1.93462$ |
$(2,a), (2,a+1), (13,a+6)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 2 \cdot 7^{2} \) |
$1$ |
$18.89430030$ |
4.687099046 |
\( -\frac{2146689}{1664} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-3{x}+3$ |
| 52.1-j1 |
52.1-j |
$3$ |
$9$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{18} \cdot 13^{2} \) |
$1.93462$ |
$(2,a), (2,a+1), (13,a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$7.974205950$ |
$0.265819283$ |
1.051664571 |
\( -\frac{10730978619193}{6656} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -460\) , \( -3830\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-460{x}-3830$ |
| 52.1-j2 |
52.1-j |
$3$ |
$9$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{6} \cdot 13^{6} \) |
$1.93462$ |
$(2,a), (2,a+1), (13,a+6)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$2.658068650$ |
$2.392373550$ |
1.051664571 |
\( -\frac{10218313}{17576} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -5\) , \( -8\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-5{x}-8$ |
| 52.1-j3 |
52.1-j |
$3$ |
$9$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{2} \cdot 13^{2} \) |
$1.93462$ |
$(2,a), (2,a+1), (13,a+6)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$0.886022883$ |
$21.53136195$ |
1.051664571 |
\( \frac{12167}{26} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}$ |
| 52.1-k1 |
52.1-k |
$1$ |
$1$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{22} \cdot 13^{2} \) |
$1.93462$ |
$(2,a), (2,a+1), (13,a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 3^{2} \) |
$0.079975725$ |
$9.192703767$ |
3.282821557 |
\( \frac{1105705513}{6656} a - \frac{5081318585}{6656} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -29 a - 112\) , \( -344 a - 1216\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-29a-112\right){x}-344a-1216$ |
| 52.1-l1 |
52.1-l |
$1$ |
$1$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{10} \cdot 13^{2} \) |
$1.93462$ |
$(2,a), (2,a+1), (13,a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$9.192703767$ |
2.280429143 |
\( -\frac{1105705513}{6656} a - \frac{248475817}{416} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -2 a - 9\) , \( 2 a + 1\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-2a-9\right){x}+2a+1$ |
| 52.1-m1 |
52.1-m |
$2$ |
$3$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{26} \cdot 13^{2} \) |
$1.93462$ |
$(2,a), (2,a+1), (13,a+6)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$13.01824364$ |
3.229428790 |
\( -\frac{5819681}{6656} a - \frac{286405}{208} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -54 a + 253\) , \( -101 a + 462\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-54a+253\right){x}-101a+462$ |
| 52.1-m2 |
52.1-m |
$2$ |
$3$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{30} \cdot 13^{6} \) |
$1.93462$ |
$(2,a), (2,a+1), (13,a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$1.446471516$ |
3.229428790 |
\( \frac{94024500233}{71991296} a - \frac{312391592857}{71991296} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 706 a - 3187\) , \( 23075 a - 104546\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(706a-3187\right){x}+23075a-104546$ |
| 52.1-n1 |
52.1-n |
$2$ |
$3$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{18} \cdot 13^{6} \) |
$1.93462$ |
$(2,a), (2,a+1), (13,a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \cdot 5 \) |
$0.234142965$ |
$1.446471516$ |
2.520493447 |
\( -\frac{94024500233}{71991296} a - \frac{13647943289}{4499456} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( -362 a + 1647\) , \( 2717 a - 12308\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-362a+1647\right){x}+2717a-12308$ |
| 52.1-n2 |
52.1-n |
$2$ |
$3$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{14} \cdot 13^{2} \) |
$1.93462$ |
$(2,a), (2,a+1), (13,a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 5 \) |
$0.078047655$ |
$13.01824364$ |
2.520493447 |
\( \frac{5819681}{6656} a - \frac{14984641}{6656} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( 53 a - 233\) , \( -535 a + 2428\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(53a-233\right){x}-535a+2428$ |
| 52.1-o1 |
52.1-o |
$1$ |
$1$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{32} \cdot 13^{4} \) |
$1.93462$ |
$(2,a), (2,a+1), (13,a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$2.930708174$ |
0.727019221 |
\( \frac{102641119396563}{90731184128} a - \frac{19477951181917}{5670699008} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 948 a - 4290\) , \( -36448 a + 165148\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(948a-4290\right){x}-36448a+165148$ |
| 52.1-p1 |
52.1-p |
$1$ |
$1$ |
\(\Q(\sqrt{65}) \) |
$2$ |
$[2, 0]$ |
52.1 |
\( 2^{2} \cdot 13 \) |
\( 2^{44} \cdot 13^{4} \) |
$1.93462$ |
$(2,a), (2,a+1), (13,a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \cdot 3 \cdot 29 \) |
$0.022004812$ |
$2.930708174$ |
5.567276826 |
\( -\frac{102641119396563}{90731184128} a - \frac{209006099514109}{90731184128} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -1191 a + 5397\) , \( 5398 a - 24458\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-1191a+5397\right){x}+5398a-24458$ |
*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.
