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 |
1568.a1 |
1568f2 |
1568.a |
1568f |
$2$ |
$2$ |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{9} \cdot 7^{9} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 3$ |
8.6.0.3, 3.3.0.1 |
2B, 3Nn |
$168$ |
$72$ |
$3$ |
$1$ |
$1$ |
|
$1$ |
$1792$ |
$0.833914$ |
$238328$ |
$[0, 1, 0, -3544, -82104]$ |
\(y^2=x^3+x^2-3544x-82104\) |
2.3.0.a.1, 3.3.0.a.1, 6.9.0.a.1, 8.6.0.e.1, 12.18.0.d.1, $\ldots$ |
$[]$ |
1568.a2 |
1568f1 |
1568.a |
1568f |
$2$ |
$2$ |
\( 2^{5} \cdot 7^{2} \) |
\( - 2^{6} \cdot 7^{9} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 3$ |
8.6.0.3, 3.3.0.1 |
2B, 3Nn |
$168$ |
$72$ |
$3$ |
$1$ |
$1$ |
|
$1$ |
$896$ |
$0.487340$ |
$-64$ |
$[0, 1, 0, -114, -2528]$ |
\(y^2=x^3+x^2-114x-2528\) |
2.3.0.a.1, 3.3.0.a.1, 6.9.0.a.1, 8.6.0.e.1, 12.18.0.e.1, $\ldots$ |
$[]$ |
1568.b1 |
1568e2 |
1568.b |
1568e |
$2$ |
$2$ |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{9} \cdot 7^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.6 |
2B |
$56$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$768$ |
$0.515755$ |
$125000/49$ |
$[0, 1, 0, -408, -1940]$ |
\(y^2=x^3+x^2-408x-1940\) |
2.3.0.a.1, 8.6.0.b.1, 28.6.0.c.1, 56.12.0.k.1 |
$[]$ |
1568.b2 |
1568e1 |
1568.b |
1568e |
$2$ |
$2$ |
\( 2^{5} \cdot 7^{2} \) |
\( - 2^{6} \cdot 7^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.1 |
2B |
$56$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$384$ |
$0.169181$ |
$8000/7$ |
$[0, 1, 0, 82, -176]$ |
\(y^2=x^3+x^2+82x-176\) |
2.3.0.a.1, 8.6.0.c.1, 14.6.0.b.1, 56.12.0.n.1 |
$[]$ |
1568.c1 |
1568i2 |
1568.c |
1568i |
$2$ |
$2$ |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{9} \cdot 7^{3} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 3$ |
8.6.0.3, 3.3.0.1 |
2B, 3Nn |
$168$ |
$72$ |
$3$ |
$2.787462980$ |
$1$ |
|
$3$ |
$256$ |
$-0.139041$ |
$238328$ |
$[0, 1, 0, -72, -260]$ |
\(y^2=x^3+x^2-72x-260\) |
2.3.0.a.1, 3.3.0.a.1, 6.9.0.a.1, 8.6.0.e.1, 12.18.0.d.1, $\ldots$ |
$[(11, 20)]$ |
1568.c2 |
1568i1 |
1568.c |
1568i |
$2$ |
$2$ |
\( 2^{5} \cdot 7^{2} \) |
\( - 2^{6} \cdot 7^{3} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 3$ |
8.6.0.3, 3.3.0.1 |
2B, 3Nn |
$168$ |
$72$ |
$3$ |
$1.393731490$ |
$1$ |
|
$5$ |
$128$ |
$-0.485614$ |
$-64$ |
$[0, 1, 0, -2, -8]$ |
\(y^2=x^3+x^2-2x-8\) |
2.3.0.a.1, 3.3.0.a.1, 6.9.0.a.1, 8.6.0.e.1, 12.18.0.e.1, $\ldots$ |
$[(4, 8)]$ |
1568.d1 |
1568b2 |
1568.d |
1568b |
$2$ |
$2$ |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{9} \) |
$0$ |
$\Z/2\Z$ |
$\Q(\sqrt{-1})$ |
$-4$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$1$ |
$1792$ |
$0.842047$ |
$1728$ |
$[0, 0, 0, -1372, 0]$ |
\(y^2=x^3-1372x\) |
|
$[]$ |
1568.d2 |
1568b1 |
1568.d |
1568b |
$2$ |
$2$ |
\( 2^{5} \cdot 7^{2} \) |
\( - 2^{6} \cdot 7^{9} \) |
$0$ |
$\Z/2\Z$ |
$\Q(\sqrt{-1})$ |
$-4$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$1$ |
$896$ |
$0.495473$ |
$1728$ |
$[0, 0, 0, 343, 0]$ |
\(y^2=x^3+343x\) |
|
$[]$ |
1568.e1 |
1568g2 |
1568.e |
1568g |
$4$ |
$4$ |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{9} \cdot 7^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q(\sqrt{-1})$ |
$-16$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1.494440753$ |
$1$ |
|
$3$ |
$384$ |
$0.355569$ |
$287496$ |
$[0, 0, 0, -539, -4802]$ |
\(y^2=x^3-539x-4802\) |
|
$[(49, 294)]$ |
1568.e2 |
1568g3 |
1568.e |
1568g |
$4$ |
$4$ |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{9} \cdot 7^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q(\sqrt{-1})$ |
$-16$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1.494440753$ |
$1$ |
|
$3$ |
$384$ |
$0.355569$ |
$287496$ |
$[0, 0, 0, -539, 4802]$ |
\(y^2=x^3-539x+4802\) |
|
$[(-14, 98)]$ |
1568.e3 |
1568g1 |
1568.e |
1568g |
$4$ |
$4$ |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{6} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q(\sqrt{-1})$ |
$-4$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$2$ |
16.192.9.143 |
2Cs |
|
|
|
$2.988881507$ |
$1$ |
|
$5$ |
$192$ |
$0.008996$ |
$1728$ |
$[0, 0, 0, -49, 0]$ |
\(y^2=x^3-49x\) |
|
$[(25, 120)]$ |
1568.e4 |
1568g4 |
1568.e |
1568g |
$4$ |
$4$ |
\( 2^{5} \cdot 7^{2} \) |
\( - 2^{12} \cdot 7^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q(\sqrt{-1})$ |
$-4$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$2$ |
16.192.9.178 |
2B |
|
|
|
$1.494440753$ |
$1$ |
|
$5$ |
$384$ |
$0.355569$ |
$1728$ |
$[0, 0, 0, 196, 0]$ |
\(y^2=x^3+196x\) |
|
$[(2, 20)]$ |
1568.f1 |
1568a2 |
1568.f |
1568a |
$2$ |
$2$ |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{3} \) |
$0$ |
$\Z/2\Z$ |
$\Q(\sqrt{-1})$ |
$-4$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$1$ |
$256$ |
$-0.130908$ |
$1728$ |
$[0, 0, 0, -28, 0]$ |
\(y^2=x^3-28x\) |
|
$[]$ |
1568.f2 |
1568a1 |
1568.f |
1568a |
$2$ |
$2$ |
\( 2^{5} \cdot 7^{2} \) |
\( - 2^{6} \cdot 7^{3} \) |
$0$ |
$\Z/2\Z$ |
$\Q(\sqrt{-1})$ |
$-4$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$1$ |
$128$ |
$-0.477482$ |
$1728$ |
$[0, 0, 0, 7, 0]$ |
\(y^2=x^3+7x\) |
|
$[]$ |
1568.g1 |
1568h2 |
1568.g |
1568h |
$2$ |
$2$ |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{9} \cdot 7^{9} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 3$ |
8.6.0.3, 3.3.0.1 |
2B, 3Nn |
$168$ |
$72$ |
$3$ |
$5.414120414$ |
$1$ |
|
$1$ |
$1792$ |
$0.833914$ |
$238328$ |
$[0, -1, 0, -3544, 82104]$ |
\(y^2=x^3-x^2-3544x+82104\) |
2.3.0.a.1, 3.3.0.a.1, 6.9.0.a.1, 8.6.0.e.1, 12.18.0.d.1, $\ldots$ |
$[(361/3, 1448/3)]$ |
1568.g2 |
1568h1 |
1568.g |
1568h |
$2$ |
$2$ |
\( 2^{5} \cdot 7^{2} \) |
\( - 2^{6} \cdot 7^{9} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 3$ |
8.6.0.3, 3.3.0.1 |
2B, 3Nn |
$168$ |
$72$ |
$3$ |
$2.707060207$ |
$1$ |
|
$3$ |
$896$ |
$0.487340$ |
$-64$ |
$[0, -1, 0, -114, 2528]$ |
\(y^2=x^3-x^2-114x+2528\) |
2.3.0.a.1, 3.3.0.a.1, 6.9.0.a.1, 8.6.0.e.1, 12.18.0.e.1, $\ldots$ |
$[(2, 48)]$ |
1568.h1 |
1568c2 |
1568.h |
1568c |
$2$ |
$2$ |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{9} \cdot 7^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.6 |
2B |
$56$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$768$ |
$0.515755$ |
$125000/49$ |
$[0, -1, 0, -408, 1940]$ |
\(y^2=x^3-x^2-408x+1940\) |
2.3.0.a.1, 8.6.0.b.1, 28.6.0.c.1, 56.12.0.k.1 |
$[]$ |
1568.h2 |
1568c1 |
1568.h |
1568c |
$2$ |
$2$ |
\( 2^{5} \cdot 7^{2} \) |
\( - 2^{6} \cdot 7^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.1 |
2B |
$56$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$384$ |
$0.169181$ |
$8000/7$ |
$[0, -1, 0, 82, 176]$ |
\(y^2=x^3-x^2+82x+176\) |
2.3.0.a.1, 8.6.0.c.1, 14.6.0.b.1, 56.12.0.n.1 |
$[]$ |
1568.i1 |
1568d2 |
1568.i |
1568d |
$2$ |
$2$ |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{9} \cdot 7^{3} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 3$ |
8.6.0.3, 3.3.0.1 |
2B, 3Nn |
$168$ |
$72$ |
$3$ |
$1$ |
$1$ |
|
$1$ |
$256$ |
$-0.139041$ |
$238328$ |
$[0, -1, 0, -72, 260]$ |
\(y^2=x^3-x^2-72x+260\) |
2.3.0.a.1, 3.3.0.a.1, 6.9.0.a.1, 8.6.0.e.1, 12.18.0.d.1, $\ldots$ |
$[]$ |
1568.i2 |
1568d1 |
1568.i |
1568d |
$2$ |
$2$ |
\( 2^{5} \cdot 7^{2} \) |
\( - 2^{6} \cdot 7^{3} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 3$ |
8.6.0.3, 3.3.0.1 |
2B, 3Nn |
$168$ |
$72$ |
$3$ |
$1$ |
$1$ |
|
$1$ |
$128$ |
$-0.485614$ |
$-64$ |
$[0, -1, 0, -2, 8]$ |
\(y^2=x^3-x^2-2x+8\) |
2.3.0.a.1, 3.3.0.a.1, 6.9.0.a.1, 8.6.0.e.1, 12.18.0.e.1, $\ldots$ |
$[]$ |