| 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 |
$abc$ quality |
Szpiro ratio |
Weierstrass coefficients |
Weierstrass equation |
mod-$m$ images |
MW-generators |
| 2175.a1 |
2175j1 |
2175.a |
2175j |
$2$ |
$5$ |
\( 3 \cdot 5^{2} \cdot 29 \) |
\( - 3 \cdot 5^{3} \cdot 29 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.24.0.3 |
5B.1.2 |
$870$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$912$ |
$0.141300$ |
$-301302001664/87$ |
$1.19848$ |
$4.06774$ |
$[0, 1, 1, -698, -7336]$ |
\(y^2+y=x^3+x^2-698x-7336\) |
5.24.0-5.a.2.2, 870.48.1.? |
$[]$ |
| 2175.a2 |
2175j2 |
2175.a |
2175j |
$2$ |
$5$ |
\( 3 \cdot 5^{2} \cdot 29 \) |
\( - 3^{5} \cdot 5^{3} \cdot 29^{5} \) |
$0$ |
$\Z/5\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.24.0.1 |
5B.1.1 |
$870$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$4$ |
$4560$ |
$0.946019$ |
$1351431663616/4984209207$ |
$1.01570$ |
$4.48183$ |
$[0, 1, 1, 1152, -34486]$ |
\(y^2+y=x^3+x^2+1152x-34486\) |
5.24.0-5.a.1.2, 870.48.1.? |
$[]$ |
| 2175.b1 |
2175c3 |
2175.b |
2175c |
$4$ |
$4$ |
\( 3 \cdot 5^{2} \cdot 29 \) |
\( 3^{2} \cdot 5^{7} \cdot 29^{4} \) |
$2$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.8 |
2B |
$1160$ |
$48$ |
$0$ |
$0.482474972$ |
$1$ |
|
$24$ |
$4608$ |
$1.042370$ |
$1888690601881/31827645$ |
$0.93261$ |
$4.93489$ |
$[1, 1, 1, -6438, -198594]$ |
\(y^2+xy+y=x^3+x^2-6438x-198594\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 10.6.0.a.1, 20.24.0-20.g.1.1, 232.24.0.?, $\ldots$ |
$[(-44, 65), (-50, 62)]$ |
| 2175.b2 |
2175c2 |
2175.b |
2175c |
$4$ |
$4$ |
\( 3 \cdot 5^{2} \cdot 29 \) |
\( 3^{4} \cdot 5^{8} \cdot 29^{2} \) |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.1 |
2Cs |
$580$ |
$48$ |
$0$ |
$1.929899890$ |
$1$ |
|
$24$ |
$2304$ |
$0.695796$ |
$3803721481/1703025$ |
$0.90376$ |
$4.12710$ |
$[1, 1, 1, -813, 3906]$ |
\(y^2+xy+y=x^3+x^2-813x+3906\) |
2.6.0.a.1, 4.12.0-2.a.1.1, 20.24.0-20.b.1.2, 116.24.0.?, 580.48.0.? |
$[(0, 62), (30, 72)]$ |
| 2175.b3 |
2175c1 |
2175.b |
2175c |
$4$ |
$4$ |
\( 3 \cdot 5^{2} \cdot 29 \) |
\( 3^{2} \cdot 5^{7} \cdot 29 \) |
$2$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.7 |
2B |
$1160$ |
$48$ |
$0$ |
$1.929899890$ |
$1$ |
|
$23$ |
$1152$ |
$0.349223$ |
$2305199161/1305$ |
$0.87163$ |
$4.06193$ |
$[1, 1, 1, -688, 6656]$ |
\(y^2+xy+y=x^3+x^2-688x+6656\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 40.24.0-40.z.1.4, 232.24.0.?, 290.6.0.?, $\ldots$ |
$[(14, -3), (11, 18)]$ |
| 2175.b4 |
2175c4 |
2175.b |
2175c |
$4$ |
$4$ |
\( 3 \cdot 5^{2} \cdot 29 \) |
\( - 3^{8} \cdot 5^{10} \cdot 29 \) |
$2$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.6 |
2B |
$1160$ |
$48$ |
$0$ |
$1.929899890$ |
$1$ |
|
$18$ |
$4608$ |
$1.042370$ |
$157376536199/118918125$ |
$0.94171$ |
$4.61152$ |
$[1, 1, 1, 2812, 32906]$ |
\(y^2+xy+y=x^3+x^2+2812x+32906\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 20.12.0-4.c.1.2, 40.24.0-40.z.1.10, $\ldots$ |
$[(20, 302), (9, 238)]$ |
| 2175.c1 |
2175e2 |
2175.c |
2175e |
$2$ |
$2$ |
\( 3 \cdot 5^{2} \cdot 29 \) |
\( 3^{2} \cdot 5^{3} \cdot 29^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$580$ |
$12$ |
$0$ |
$0.319074969$ |
$1$ |
|
$10$ |
$384$ |
$0.090849$ |
$12698260037/7569$ |
$0.91772$ |
$3.65567$ |
$[1, 1, 1, -243, 1356]$ |
\(y^2+xy+y=x^3+x^2-243x+1356\) |
2.3.0.a.1, 10.6.0.a.1, 116.6.0.?, 580.12.0.? |
$[(10, 2)]$ |
| 2175.c2 |
2175e1 |
2175.c |
2175e |
$2$ |
$2$ |
\( 3 \cdot 5^{2} \cdot 29 \) |
\( 3^{4} \cdot 5^{3} \cdot 29 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$580$ |
$12$ |
$0$ |
$0.638149939$ |
$1$ |
|
$7$ |
$192$ |
$-0.255725$ |
$5177717/2349$ |
$0.85504$ |
$2.64005$ |
$[1, 1, 1, -18, 6]$ |
\(y^2+xy+y=x^3+x^2-18x+6\) |
2.3.0.a.1, 20.6.0.c.1, 116.6.0.?, 290.6.0.?, 580.12.0.? |
$[(0, 2)]$ |
| 2175.d1 |
2175a1 |
2175.d |
2175a |
$2$ |
$3$ |
\( 3 \cdot 5^{2} \cdot 29 \) |
\( - 3^{3} \cdot 5^{7} \cdot 29 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$870$ |
$16$ |
$0$ |
$0.269557008$ |
$1$ |
|
$4$ |
$480$ |
$0.279546$ |
$-160989184/3915$ |
$0.86981$ |
$3.72094$ |
$[0, -1, 1, -283, 1968]$ |
\(y^2+y=x^3-x^2-283x+1968\) |
3.4.0.a.1, 15.8.0-3.a.1.2, 174.8.0.?, 870.16.0.? |
$[(12, 12)]$ |
| 2175.d2 |
2175a2 |
2175.d |
2175a |
$2$ |
$3$ |
\( 3 \cdot 5^{2} \cdot 29 \) |
\( - 3 \cdot 5^{9} \cdot 29^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$870$ |
$16$ |
$0$ |
$0.808671026$ |
$1$ |
|
$4$ |
$1440$ |
$0.828853$ |
$12747309056/9145875$ |
$0.97110$ |
$4.28447$ |
$[0, -1, 1, 1217, 7593]$ |
\(y^2+y=x^3-x^2+1217x+7593\) |
3.4.0.a.1, 15.8.0-3.a.1.1, 174.8.0.?, 870.16.0.? |
$[(-3, 62)]$ |
| 2175.e1 |
2175d1 |
2175.e |
2175d |
$1$ |
$1$ |
\( 3 \cdot 5^{2} \cdot 29 \) |
\( - 3^{7} \cdot 5^{8} \cdot 29^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$0.424252168$ |
$1$ |
|
$4$ |
$1680$ |
$1.011440$ |
$-15947530240/1839267$ |
$0.99256$ |
$4.75613$ |
$[0, -1, 1, -3833, 101318]$ |
\(y^2+y=x^3-x^2-3833x+101318\) |
6.2.0.a.1 |
$[(-8, 362)]$ |
| 2175.f1 |
2175g1 |
2175.f |
2175g |
$1$ |
$1$ |
\( 3 \cdot 5^{2} \cdot 29 \) |
\( - 3^{7} \cdot 5^{2} \cdot 29^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$0.109229930$ |
$1$ |
|
$6$ |
$336$ |
$0.206722$ |
$-15947530240/1839267$ |
$0.99256$ |
$3.49954$ |
$[0, 1, 1, -153, 749]$ |
\(y^2+y=x^3+x^2-153x+749\) |
6.2.0.a.1 |
$[(27, 130)]$ |
| 2175.g1 |
2175h1 |
2175.g |
2175h |
$1$ |
$1$ |
\( 3 \cdot 5^{2} \cdot 29 \) |
\( - 3^{5} \cdot 5^{13} \cdot 29 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$870$ |
$2$ |
$0$ |
$0.436544531$ |
$1$ |
|
$4$ |
$3360$ |
$1.163013$ |
$53838872576/550546875$ |
$1.03969$ |
$4.83807$ |
$[0, 1, 1, 1967, -136406]$ |
\(y^2+y=x^3+x^2+1967x-136406\) |
870.2.0.? |
$[(278, 4687)]$ |
| 2175.h1 |
2175b3 |
2175.h |
2175b |
$4$ |
$4$ |
\( 3 \cdot 5^{2} \cdot 29 \) |
\( 3^{2} \cdot 5^{7} \cdot 29 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.10 |
2B |
$6960$ |
$192$ |
$3$ |
$1$ |
$4$ |
$2$ |
$0$ |
$7680$ |
$1.348839$ |
$37286818682653441/1305$ |
$1.23338$ |
$6.22191$ |
$[1, 1, 0, -174000, -28009125]$ |
\(y^2+xy=x^3+x^2-174000x-28009125\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.o.1, 20.12.0-4.c.1.1, 40.24.0-8.o.1.3, $\ldots$ |
$[]$ |
| 2175.h2 |
2175b2 |
2175.h |
2175b |
$4$ |
$4$ |
\( 3 \cdot 5^{2} \cdot 29 \) |
\( 3^{4} \cdot 5^{8} \cdot 29^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.4 |
2Cs |
$3480$ |
$192$ |
$3$ |
$1$ |
$4$ |
$2$ |
$2$ |
$3840$ |
$1.002264$ |
$9104453457841/1703025$ |
$1.03605$ |
$5.13956$ |
$[1, 1, 0, -10875, -441000]$ |
\(y^2+xy=x^3+x^2-10875x-441000\) |
2.6.0.a.1, 4.12.0.a.1, 20.24.0-4.a.1.1, 24.24.0.j.1, 116.24.0.?, $\ldots$ |
$[]$ |
| 2175.h3 |
2175b4 |
2175.h |
2175b |
$4$ |
$4$ |
\( 3 \cdot 5^{2} \cdot 29 \) |
\( - 3^{2} \cdot 5^{10} \cdot 29^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.9 |
2B |
$6960$ |
$192$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$7680$ |
$1.348839$ |
$-6561258219361/3978455625$ |
$0.95298$ |
$5.19020$ |
$[1, 1, 0, -9750, -534375]$ |
\(y^2+xy=x^3+x^2-9750x-534375\) |
2.3.0.a.1, 4.12.0.d.1, 20.24.0-4.d.1.1, 24.24.0.z.1, 120.48.0.?, $\ldots$ |
$[]$ |
| 2175.h4 |
2175b1 |
2175.h |
2175b |
$4$ |
$4$ |
\( 3 \cdot 5^{2} \cdot 29 \) |
\( 3^{8} \cdot 5^{7} \cdot 29 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.10 |
2B |
$6960$ |
$192$ |
$3$ |
$1$ |
$1$ |
|
$1$ |
$1920$ |
$0.655691$ |
$2992209121/951345$ |
$0.88867$ |
$4.09587$ |
$[1, 1, 0, -750, -5625]$ |
\(y^2+xy=x^3+x^2-750x-5625\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.o.1, 20.12.0-4.c.1.2, 40.24.0-8.o.1.1, $\ldots$ |
$[]$ |
| 2175.i1 |
2175i2 |
2175.i |
2175i |
$2$ |
$2$ |
\( 3 \cdot 5^{2} \cdot 29 \) |
\( 3^{2} \cdot 5^{9} \cdot 29^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$580$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1920$ |
$0.895568$ |
$12698260037/7569$ |
$0.91772$ |
$4.91226$ |
$[1, 0, 1, -6076, 181673]$ |
\(y^2+xy+y=x^3-6076x+181673\) |
2.3.0.a.1, 10.6.0.a.1, 116.6.0.?, 580.12.0.? |
$[]$ |
| 2175.i2 |
2175i1 |
2175.i |
2175i |
$2$ |
$2$ |
\( 3 \cdot 5^{2} \cdot 29 \) |
\( 3^{4} \cdot 5^{9} \cdot 29 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$580$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$960$ |
$0.548994$ |
$5177717/2349$ |
$0.85504$ |
$3.89664$ |
$[1, 0, 1, -451, 1673]$ |
\(y^2+xy+y=x^3-451x+1673\) |
2.3.0.a.1, 20.6.0.c.1, 116.6.0.?, 290.6.0.?, 580.12.0.? |
$[]$ |
| 2175.j1 |
2175f1 |
2175.j |
2175f |
$2$ |
$5$ |
\( 3 \cdot 5^{2} \cdot 29 \) |
\( - 3 \cdot 5^{9} \cdot 29 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.24.0.4 |
5B.1.3 |
$870$ |
$48$ |
$1$ |
$11.92681209$ |
$1$ |
|
$0$ |
$4560$ |
$0.946019$ |
$-301302001664/87$ |
$1.19848$ |
$5.32433$ |
$[0, -1, 1, -17458, -882057]$ |
\(y^2+y=x^3-x^2-17458x-882057\) |
5.24.0-5.a.2.1, 870.48.1.? |
$[(1180533/82, 659971191/82)]$ |
| 2175.j2 |
2175f2 |
2175.j |
2175f |
$2$ |
$5$ |
\( 3 \cdot 5^{2} \cdot 29 \) |
\( - 3^{5} \cdot 5^{9} \cdot 29^{5} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.24.0.2 |
5B.1.4 |
$870$ |
$48$ |
$1$ |
$2.385362418$ |
$1$ |
|
$0$ |
$22800$ |
$1.750738$ |
$1351431663616/4984209207$ |
$1.01570$ |
$5.73842$ |
$[0, -1, 1, 28792, -4368307]$ |
\(y^2+y=x^3-x^2+28792x-4368307\) |
5.24.0-5.a.1.1, 870.48.1.? |
$[(6493/2, 525621/2)]$ |
