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 |
389.a1 |
389a1 |
389.a |
389a |
$1$ |
$1$ |
\( 389 \) |
\( 389 \) |
$2$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$778$ |
$2$ |
$0$ |
$0.152460177$ |
$1$ |
|
$20$ |
$40$ |
$-0.795642$ |
$1404928/389$ |
$[0, 1, 1, -2, 0]$ |
\(y^2+y=x^3+x^2-2x\) |
778.2.0.? |
$[(0, 0), (1, 0)]$ |
3501.c1 |
3501b1 |
3501.c |
3501b |
$1$ |
$1$ |
\( 3^{2} \cdot 389 \) |
\( 3^{6} \cdot 389 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$778$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$960$ |
$-0.246336$ |
$1404928/389$ |
$[0, 0, 1, -21, -27]$ |
\(y^2+y=x^3-21x-27\) |
778.2.0.? |
$[]$ |
6224.d1 |
6224d1 |
6224.d |
6224d |
$1$ |
$1$ |
\( 2^{4} \cdot 389 \) |
\( 2^{12} \cdot 389 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$778$ |
$2$ |
$0$ |
$2.706921757$ |
$1$ |
|
$2$ |
$1600$ |
$-0.102494$ |
$1404928/389$ |
$[0, -1, 0, -37, -51]$ |
\(y^2=x^3-x^2-37x-51\) |
778.2.0.? |
$[(12, 33)]$ |
9725.a1 |
9725a1 |
9725.a |
9725a |
$1$ |
$1$ |
\( 5^{2} \cdot 389 \) |
\( 5^{6} \cdot 389 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$778$ |
$2$ |
$0$ |
$1$ |
$4$ |
$2$ |
$0$ |
$4320$ |
$0.009077$ |
$1404928/389$ |
$[0, -1, 1, -58, 143]$ |
\(y^2+y=x^3-x^2-58x+143\) |
778.2.0.? |
$[]$ |
19061.a1 |
19061a1 |
19061.a |
19061a |
$1$ |
$1$ |
\( 7^{2} \cdot 389 \) |
\( 7^{6} \cdot 389 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$778$ |
$2$ |
$0$ |
$2.967669191$ |
$1$ |
|
$2$ |
$9360$ |
$0.177313$ |
$1404928/389$ |
$[0, -1, 1, -114, -302]$ |
\(y^2+y=x^3-x^2-114x-302\) |
778.2.0.? |
$[(14, 25)]$ |
24896.b1 |
24896f1 |
24896.b |
24896f |
$1$ |
$1$ |
\( 2^{6} \cdot 389 \) |
\( 2^{6} \cdot 389 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$778$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$3200$ |
$-0.449068$ |
$1404928/389$ |
$[0, 1, 0, -9, -11]$ |
\(y^2=x^3+x^2-9x-11\) |
778.2.0.? |
$[]$ |
24896.g1 |
24896b1 |
24896.g |
24896b |
$1$ |
$1$ |
\( 2^{6} \cdot 389 \) |
\( 2^{6} \cdot 389 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$778$ |
$2$ |
$0$ |
$2.342729208$ |
$1$ |
|
$0$ |
$3200$ |
$-0.449068$ |
$1404928/389$ |
$[0, -1, 0, -9, 11]$ |
\(y^2=x^3-x^2-9x+11\) |
778.2.0.? |
$[(5/2, 3/2)]$ |
47069.h1 |
47069h1 |
47069.h |
47069h |
$1$ |
$1$ |
\( 11^{2} \cdot 389 \) |
\( 11^{6} \cdot 389 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$778$ |
$2$ |
$0$ |
$1.668812575$ |
$1$ |
|
$0$ |
$51200$ |
$0.403306$ |
$1404928/389$ |
$[0, 1, 1, -282, -1413]$ |
\(y^2+y=x^3+x^2-282x-1413\) |
778.2.0.? |
$[(-27/2, 117/2)]$ |
56016.i1 |
56016g1 |
56016.i |
56016g |
$1$ |
$1$ |
\( 2^{4} \cdot 3^{2} \cdot 389 \) |
\( 2^{12} \cdot 3^{6} \cdot 389 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$778$ |
$2$ |
$0$ |
$3.148033937$ |
$1$ |
|
$2$ |
$38400$ |
$0.446812$ |
$1404928/389$ |
$[0, 0, 0, -336, 1712]$ |
\(y^2=x^3-336x+1712\) |
778.2.0.? |
$[(-7, 61)]$ |
65741.e1 |
65741c1 |
65741.e |
65741c |
$1$ |
$1$ |
\( 13^{2} \cdot 389 \) |
\( 13^{6} \cdot 389 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$778$ |
$2$ |
$0$ |
$1$ |
$4$ |
$2$ |
$0$ |
$89760$ |
$0.486833$ |
$1404928/389$ |
$[0, 1, 1, -394, 2045]$ |
\(y^2+y=x^3+x^2-394x+2045\) |
778.2.0.? |
$[]$ |
87525.i1 |
87525t1 |
87525.i |
87525t |
$1$ |
$1$ |
\( 3^{2} \cdot 5^{2} \cdot 389 \) |
\( 3^{6} \cdot 5^{6} \cdot 389 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$778$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$103680$ |
$0.558383$ |
$1404928/389$ |
$[0, 0, 1, -525, -3344]$ |
\(y^2+y=x^3-525x-3344\) |
778.2.0.? |
$[]$ |
112421.a1 |
112421c1 |
112421.a |
112421c |
$1$ |
$1$ |
\( 17^{2} \cdot 389 \) |
\( 17^{6} \cdot 389 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$778$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$184320$ |
$0.620965$ |
$1404928/389$ |
$[0, -1, 1, -674, 5092]$ |
\(y^2+y=x^3-x^2-674x+5092\) |
778.2.0.? |
$[]$ |
140429.a1 |
140429a1 |
140429.a |
140429a |
$1$ |
$1$ |
\( 19^{2} \cdot 389 \) |
\( 19^{6} \cdot 389 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$778$ |
$2$ |
$0$ |
$10.03169539$ |
$1$ |
|
$0$ |
$270000$ |
$0.676578$ |
$1404928/389$ |
$[0, -1, 1, -842, -6515]$ |
\(y^2+y=x^3-x^2-842x-6515\) |
778.2.0.? |
$[(21181/10, 3044629/10)]$ |
151321.a1 |
151321a1 |
151321.a |
151321a |
$1$ |
$1$ |
\( 389^{2} \) |
\( 389^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$778$ |
$2$ |
$0$ |
$8.116888144$ |
$1$ |
|
$0$ |
$6052800$ |
$2.186150$ |
$1404928/389$ |
$[0, -1, 1, -353082, 58436527]$ |
\(y^2+y=x^3-x^2-353082x+58436527\) |
778.2.0.? |
$[(2861/2, 104699/2)]$ |
155600.a1 |
155600b1 |
155600.a |
155600b |
$1$ |
$1$ |
\( 2^{4} \cdot 5^{2} \cdot 389 \) |
\( 2^{12} \cdot 5^{6} \cdot 389 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$778$ |
$2$ |
$0$ |
$4.261331550$ |
$1$ |
|
$2$ |
$172800$ |
$0.702225$ |
$1404928/389$ |
$[0, 1, 0, -933, -8237]$ |
\(y^2=x^3+x^2-933x-8237\) |
778.2.0.? |
$[(54, 319)]$ |
171549.c1 |
171549c1 |
171549.c |
171549c |
$1$ |
$1$ |
\( 3^{2} \cdot 7^{2} \cdot 389 \) |
\( 3^{6} \cdot 7^{6} \cdot 389 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$778$ |
$2$ |
$0$ |
$5.257773782$ |
$1$ |
|
$0$ |
$224640$ |
$0.726620$ |
$1404928/389$ |
$[0, 0, 1, -1029, 9175]$ |
\(y^2+y=x^3-1029x+9175\) |
778.2.0.? |
$[(-103/2, 1087/2)]$ |
205781.a1 |
205781a1 |
205781.a |
205781a |
$1$ |
$1$ |
\( 23^{2} \cdot 389 \) |
\( 23^{6} \cdot 389 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$778$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$492800$ |
$0.772105$ |
$1404928/389$ |
$[0, 1, 1, -1234, -12466]$ |
\(y^2+y=x^3+x^2-1234x-12466\) |
778.2.0.? |
$[]$ |
224064.a1 |
224064l1 |
224064.a |
224064l |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{2} \cdot 389 \) |
\( 2^{6} \cdot 3^{6} \cdot 389 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$778$ |
$2$ |
$0$ |
$1.026840297$ |
$1$ |
|
$2$ |
$76800$ |
$0.100238$ |
$1404928/389$ |
$[0, 0, 0, -84, -214]$ |
\(y^2=x^3-84x-214\) |
778.2.0.? |
$[(-5, 9)]$ |
224064.h1 |
224064d1 |
224064.h |
224064d |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{2} \cdot 389 \) |
\( 2^{6} \cdot 3^{6} \cdot 389 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$778$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$76800$ |
$0.100238$ |
$1404928/389$ |
$[0, 0, 0, -84, 214]$ |
\(y^2=x^3-84x+214\) |
778.2.0.? |
$[]$ |
304976.b1 |
304976b1 |
304976.b |
304976b |
$1$ |
$1$ |
\( 2^{4} \cdot 7^{2} \cdot 389 \) |
\( 2^{12} \cdot 7^{6} \cdot 389 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$778$ |
$2$ |
$0$ |
$1$ |
$4$ |
$2$ |
$0$ |
$374400$ |
$0.870461$ |
$1404928/389$ |
$[0, 1, 0, -1829, 21139]$ |
\(y^2=x^3+x^2-1829x+21139\) |
778.2.0.? |
$[]$ |
327149.a1 |
327149a1 |
327149.a |
327149a |
$1$ |
$1$ |
\( 29^{2} \cdot 389 \) |
\( 29^{6} \cdot 389 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$778$ |
$2$ |
$0$ |
$6.313426449$ |
$1$ |
|
$0$ |
$967680$ |
$0.888006$ |
$1404928/389$ |
$[0, -1, 1, -1962, 24817]$ |
\(y^2+y=x^3-x^2-1962x+24817\) |
778.2.0.? |
$[(509/2, 10787/2)]$ |
373829.a1 |
373829a1 |
373829.a |
373829a |
$1$ |
$1$ |
\( 31^{2} \cdot 389 \) |
\( 31^{6} \cdot 389 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$778$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1209600$ |
$0.921352$ |
$1404928/389$ |
$[0, -1, 1, -2242, -28768]$ |
\(y^2+y=x^3-x^2-2242x-28768\) |
778.2.0.? |
$[]$ |
423621.h1 |
423621h1 |
423621.h |
423621h |
$1$ |
$1$ |
\( 3^{2} \cdot 11^{2} \cdot 389 \) |
\( 3^{6} \cdot 11^{6} \cdot 389 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$778$ |
$2$ |
$0$ |
$0.982687924$ |
$1$ |
|
$4$ |
$1228800$ |
$0.952612$ |
$1404928/389$ |
$[0, 0, 1, -2541, 35604]$ |
\(y^2+y=x^3-2541x+35604\) |
778.2.0.? |
$[(77, 544)]$ |
476525.g1 |
476525g1 |
476525.g |
476525g |
$1$ |
$1$ |
\( 5^{2} \cdot 7^{2} \cdot 389 \) |
\( 5^{6} \cdot 7^{6} \cdot 389 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$778$ |
$2$ |
$0$ |
$6.195043058$ |
$1$ |
|
$0$ |
$1010880$ |
$0.982033$ |
$1404928/389$ |
$[0, 1, 1, -2858, -43431]$ |
\(y^2+y=x^3+x^2-2858x-43431\) |
778.2.0.? |
$[(373/2, 5707/2)]$ |