Label |
Cremona label |
Class |
Cremona class |
Class size |
Class degree |
Conductor |
Discriminant |
Rank |
Torsion |
$\textrm{End}^0(E_{\overline\Q})$ |
CM |
Sato-Tate |
Semistable |
Potentially good |
Nonmax $\ell$ |
$\ell$-adic images |
mod-$\ell$ images |
Adelic level |
Adelic index |
Adelic genus |
Regulator |
$Ш_{\textrm{an}}$ |
Ш primes |
Integral points |
Modular degree |
Faltings height |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
mod-$m$ images |
MW-generators |
17986.a1 |
17986c2 |
17986.a |
17986c |
$2$ |
$2$ |
\( 2 \cdot 17 \cdot 23^{2} \) |
\( 2^{3} \cdot 17^{2} \cdot 23^{8} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.6 |
2B |
$3128$ |
$12$ |
$0$ |
$1.612221739$ |
$1$ |
|
$6$ |
$76032$ |
$1.443983$ |
$4549540393/1223048$ |
$[1, 0, 1, -18262, -696576]$ |
\(y^2+xy+y=x^3-18262x-696576\) |
2.3.0.a.1, 8.6.0.b.1, 1564.6.0.?, 3128.12.0.? |
$[(-48, 288)]$ |
17986.a2 |
17986c1 |
17986.a |
17986c |
$2$ |
$2$ |
\( 2 \cdot 17 \cdot 23^{2} \) |
\( - 2^{6} \cdot 17 \cdot 23^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.1 |
2B |
$3128$ |
$12$ |
$0$ |
$3.224443478$ |
$1$ |
|
$5$ |
$38016$ |
$1.097410$ |
$18191447/25024$ |
$[1, 0, 1, 2898, -70240]$ |
\(y^2+xy+y=x^3+2898x-70240\) |
2.3.0.a.1, 8.6.0.c.1, 782.6.0.?, 3128.12.0.? |
$[(29, 181)]$ |
17986.b1 |
17986b1 |
17986.b |
17986b |
$1$ |
$1$ |
\( 2 \cdot 17 \cdot 23^{2} \) |
\( - 2^{9} \cdot 17^{3} \cdot 23^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.18.0.1 |
3Ns |
$28152$ |
$72$ |
$3$ |
$7.463850905$ |
$1$ |
|
$0$ |
$317952$ |
$2.300472$ |
$-11466731375/2515456$ |
$[1, 0, 1, -571596, -195380214]$ |
\(y^2+xy+y=x^3-571596x-195380214\) |
3.6.0.b.1, 9.18.0.a.1, 69.12.0.a.1, 207.36.0.?, 408.12.0.?, $\ldots$ |
$[(1170526/15, 1243319254/15)]$ |
17986.c1 |
17986a1 |
17986.c |
17986a |
$1$ |
$1$ |
\( 2 \cdot 17 \cdot 23^{2} \) |
\( - 2^{9} \cdot 17^{3} \cdot 23^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.18.0.1 |
3Ns |
$28152$ |
$72$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$13824$ |
$0.732727$ |
$-11466731375/2515456$ |
$[1, 0, 1, -1081, 15964]$ |
\(y^2+xy+y=x^3-1081x+15964\) |
3.6.0.b.1, 9.18.0.a.1, 69.12.0.a.1, 207.36.0.?, 408.12.0.?, $\ldots$ |
$[]$ |
17986.d1 |
17986k2 |
17986.d |
17986k |
$2$ |
$2$ |
\( 2 \cdot 17 \cdot 23^{2} \) |
\( 2^{7} \cdot 17^{2} \cdot 23^{14} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.6 |
2B |
$136$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$3548160$ |
$3.315895$ |
$109906713160213524625/2896879967514752$ |
$[1, 0, 0, -52790508, 144226855696]$ |
\(y^2+xy=x^3-52790508x+144226855696\) |
2.3.0.a.1, 8.6.0.b.1, 68.6.0.c.1, 136.12.0.? |
$[]$ |
17986.d2 |
17986k1 |
17986.d |
17986k |
$2$ |
$2$ |
\( 2 \cdot 17 \cdot 23^{2} \) |
\( 2^{14} \cdot 17 \cdot 23^{10} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.1 |
2B |
$136$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$1774080$ |
$2.969318$ |
$107805659942195988625/77943554048$ |
$[1, 0, 0, -52451948, 146210072464]$ |
\(y^2+xy=x^3-52451948x+146210072464\) |
2.3.0.a.1, 8.6.0.c.1, 34.6.0.a.1, 136.12.0.? |
$[]$ |
17986.e1 |
17986j4 |
17986.e |
17986j |
$4$ |
$6$ |
\( 2 \cdot 17 \cdot 23^{2} \) |
\( 2 \cdot 17^{6} \cdot 23^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.6, 3.4.0.1 |
2B, 3B |
$9384$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$152064$ |
$1.747234$ |
$159661140625/48275138$ |
$[1, 0, 0, -59788, 3883374]$ |
\(y^2+xy=x^3-59788x+3883374\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.b.1, 24.24.0.y.1, $\ldots$ |
$[]$ |
17986.e2 |
17986j3 |
17986.e |
17986j |
$4$ |
$6$ |
\( 2 \cdot 17 \cdot 23^{2} \) |
\( 2^{2} \cdot 17^{3} \cdot 23^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.1, 3.4.0.1 |
2B, 3B |
$9384$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$76032$ |
$1.400661$ |
$120920208625/19652$ |
$[1, 0, 0, -54498, 4891648]$ |
\(y^2+xy=x^3-54498x+4891648\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.c.1, 24.24.0.bw.1, $\ldots$ |
$[]$ |
17986.e3 |
17986j2 |
17986.e |
17986j |
$4$ |
$6$ |
\( 2 \cdot 17 \cdot 23^{2} \) |
\( 2^{3} \cdot 17^{2} \cdot 23^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.6, 3.4.0.1 |
2B, 3B |
$9384$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$50688$ |
$1.197927$ |
$8805624625/2312$ |
$[1, 0, 0, -22758, -1323044]$ |
\(y^2+xy=x^3-22758x-1323044\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.b.1, 24.24.0.y.1, $\ldots$ |
$[]$ |
17986.e4 |
17986j1 |
17986.e |
17986j |
$4$ |
$6$ |
\( 2 \cdot 17 \cdot 23^{2} \) |
\( 2^{6} \cdot 17 \cdot 23^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.1, 3.4.0.1 |
2B, 3B |
$9384$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$25344$ |
$0.851355$ |
$3048625/1088$ |
$[1, 0, 0, -1598, -15356]$ |
\(y^2+xy=x^3-1598x-15356\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.c.1, 24.24.0.bw.1, $\ldots$ |
$[]$ |
17986.f1 |
17986h1 |
17986.f |
17986h |
$1$ |
$1$ |
\( 2 \cdot 17 \cdot 23^{2} \) |
\( - 2^{8} \cdot 17^{2} \cdot 23^{2} \) |
$2$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.2.0.1 |
|
$3128$ |
$4$ |
$0$ |
$0.307159018$ |
$1$ |
|
$14$ |
$6144$ |
$0.136784$ |
$-1364337/73984$ |
$[1, -1, 1, -19, 307]$ |
\(y^2+xy+y=x^3-x^2-19x+307\) |
4.2.0.a.1, 3128.4.0.? |
$[(1, 16), (35, 186)]$ |
17986.g1 |
17986e3 |
17986.g |
17986e |
$4$ |
$4$ |
\( 2 \cdot 17 \cdot 23^{2} \) |
\( 2^{5} \cdot 17^{4} \cdot 23^{8} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.15 |
2B |
$3128$ |
$48$ |
$0$ |
$2.839160640$ |
$1$ |
|
$0$ |
$844800$ |
$2.864357$ |
$81399873824350973793/1413843488$ |
$[1, -1, 1, -47762716, 127063975487]$ |
\(y^2+xy+y=x^3-x^2-47762716x+127063975487\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.k.1, 92.12.0.?, 136.24.0.?, $\ldots$ |
$[(34945/3, 263911/3)]$ |
17986.g2 |
17986e2 |
17986.g |
17986e |
$4$ |
$4$ |
\( 2 \cdot 17 \cdot 23^{2} \) |
\( 2^{10} \cdot 17^{2} \cdot 23^{10} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.3 |
2Cs |
$3128$ |
$48$ |
$0$ |
$5.678321280$ |
$1$ |
|
$6$ |
$422400$ |
$2.517784$ |
$19932710512768353/82815026176$ |
$[1, -1, 1, -2988156, 1981764671]$ |
\(y^2+xy+y=x^3-x^2-2988156x+1981764671\) |
2.6.0.a.1, 8.12.0.a.1, 68.12.0.b.1, 92.12.0.?, 136.24.0.?, $\ldots$ |
$[(1047, -251)]$ |
17986.g3 |
17986e4 |
17986.g |
17986e |
$4$ |
$4$ |
\( 2 \cdot 17 \cdot 23^{2} \) |
\( - 2^{5} \cdot 17 \cdot 23^{14} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.9 |
2B |
$3128$ |
$48$ |
$0$ |
$11.35664256$ |
$1$ |
|
$0$ |
$844800$ |
$2.864357$ |
$-2778067622280033/42601175992864$ |
$[1, -1, 1, -1549276, 3892597311]$ |
\(y^2+xy+y=x^3-x^2-1549276x+3892597311\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 136.24.0.?, 184.24.0.?, $\ldots$ |
$[(-92585/7, 3223331/7)]$ |
17986.g4 |
17986e1 |
17986.g |
17986e |
$4$ |
$4$ |
\( 2 \cdot 17 \cdot 23^{2} \) |
\( 2^{20} \cdot 17 \cdot 23^{8} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.9 |
2B |
$3128$ |
$48$ |
$0$ |
$2.839160640$ |
$1$ |
|
$7$ |
$211200$ |
$2.171207$ |
$16342588257633/9429843968$ |
$[1, -1, 1, -279676, -3009473]$ |
\(y^2+xy+y=x^3-x^2-279676x-3009473\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 34.6.0.a.1, 68.12.0.g.1, $\ldots$ |
$[(-11, 261)]$ |
17986.h1 |
17986g1 |
17986.h |
17986g |
$1$ |
$1$ |
\( 2 \cdot 17 \cdot 23^{2} \) |
\( - 2^{2} \cdot 17^{4} \cdot 23^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.16.0.2 |
|
$4$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$123648$ |
$1.960043$ |
$-26397808929/334084$ |
$[1, -1, 1, -265393, 53262373]$ |
\(y^2+xy+y=x^3-x^2-265393x+53262373\) |
4.16.0-4.b.1.1 |
$[]$ |
17986.i1 |
17986d1 |
17986.i |
17986d |
$1$ |
$1$ |
\( 2 \cdot 17 \cdot 23^{2} \) |
\( - 2^{2} \cdot 17^{4} \cdot 23^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.8.0.2 |
|
$92$ |
$16$ |
$0$ |
$3.900633657$ |
$1$ |
|
$0$ |
$5376$ |
$0.392295$ |
$-26397808929/334084$ |
$[1, -1, 1, -502, -4247]$ |
\(y^2+xy+y=x^3-x^2-502x-4247\) |
4.8.0.b.1, 92.16.0.? |
$[(637/4, 11121/4)]$ |
17986.j1 |
17986f1 |
17986.j |
17986f |
$1$ |
$1$ |
\( 2 \cdot 17 \cdot 23^{2} \) |
\( - 2^{8} \cdot 17^{2} \cdot 23^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.2.0.1 |
|
$136$ |
$4$ |
$0$ |
$1.000818946$ |
$1$ |
|
$2$ |
$141312$ |
$1.704531$ |
$-1364337/73984$ |
$[1, -1, 1, -9886, -3679187]$ |
\(y^2+xy+y=x^3-x^2-9886x-3679187\) |
4.2.0.a.1, 136.4.0.? |
$[(397, 7207)]$ |
17986.k1 |
17986i1 |
17986.k |
17986i |
$1$ |
$1$ |
\( 2 \cdot 17 \cdot 23^{2} \) |
\( - 2^{3} \cdot 17 \cdot 23^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$3128$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$88704$ |
$1.258717$ |
$-23912763841/3128$ |
$[1, 0, 0, -31751, 2175233]$ |
\(y^2+xy=x^3-31751x+2175233\) |
3128.2.0.? |
$[]$ |
17986.l1 |
17986l1 |
17986.l |
17986l |
$1$ |
$1$ |
\( 2 \cdot 17 \cdot 23^{2} \) |
\( - 2 \cdot 17 \cdot 23^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$3128$ |
$2$ |
$0$ |
$1$ |
$9$ |
$3$ |
$0$ |
$21120$ |
$0.802104$ |
$3375/782$ |
$[1, -1, 1, 165, -16391]$ |
\(y^2+xy+y=x^3-x^2+165x-16391\) |
3128.2.0.? |
$[]$ |