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 |
Regulator |
$Ш_{\textrm{an}}$ |
Ш primes |
Integral points |
Modular degree |
Faltings height |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
4025.a1 |
4025d1 |
4025.a |
4025d |
$1$ |
$1$ |
\( 5^{2} \cdot 7 \cdot 23 \) |
\( - 5^{7} \cdot 7^{3} \cdot 23^{2} \) |
$2$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$0.064723565$ |
$1$ |
|
$34$ |
$8640$ |
$0.633570$ |
$-242970624/907235$ |
$[0, 0, 1, -325, 6156]$ |
\(y^2+y=x^3-325x+6156\) |
4025.b1 |
4025e1 |
4025.b |
4025e |
$1$ |
$1$ |
\( 5^{2} \cdot 7 \cdot 23 \) |
\( - 5^{11} \cdot 7^{11} \cdot 23^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$0.168464283$ |
$1$ |
|
$8$ |
$137280$ |
$2.465557$ |
$1346216501445963776/3268768272021875$ |
$[0, 1, 1, 575092, 300275344]$ |
\(y^2+y=x^3+x^2+575092x+300275344\) |
4025.c1 |
4025g1 |
4025.c |
4025g |
$1$ |
$1$ |
\( 5^{2} \cdot 7 \cdot 23 \) |
\( - 5^{3} \cdot 7 \cdot 23^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$0.210484398$ |
$1$ |
|
$6$ |
$544$ |
$0.119613$ |
$-35806478336/3703$ |
$[0, -1, 1, -343, 2563]$ |
\(y^2+y=x^3-x^2-343x+2563\) |
4025.d1 |
4025f1 |
4025.d |
4025f |
$1$ |
$1$ |
\( 5^{2} \cdot 7 \cdot 23 \) |
\( - 5^{9} \cdot 7 \cdot 23^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$0.657925041$ |
$1$ |
|
$4$ |
$2720$ |
$0.924332$ |
$-35806478336/3703$ |
$[0, 1, 1, -8583, 303244]$ |
\(y^2+y=x^3+x^2-8583x+303244\) |
4025.e1 |
4025a3 |
4025.e |
4025a |
$4$ |
$4$ |
\( 5^{2} \cdot 7 \cdot 23 \) |
\( 5^{6} \cdot 7^{4} \cdot 23 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$1$ |
$1$ |
|
$0$ |
$2560$ |
$0.699085$ |
$209267191953/55223$ |
$[1, -1, 0, -3092, 66941]$ |
\(y^2+xy=x^3-x^2-3092x+66941\) |
4025.e2 |
4025a2 |
4025.e |
4025a |
$4$ |
$4$ |
\( 5^{2} \cdot 7 \cdot 23 \) |
\( 5^{6} \cdot 7^{2} \cdot 23^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.6.0.1 |
2Cs |
$1$ |
$1$ |
|
$2$ |
$1280$ |
$0.352511$ |
$72511713/25921$ |
$[1, -1, 0, -217, 816]$ |
\(y^2+xy=x^3-x^2-217x+816\) |
4025.e3 |
4025a1 |
4025.e |
4025a |
$4$ |
$4$ |
\( 5^{2} \cdot 7 \cdot 23 \) |
\( 5^{6} \cdot 7 \cdot 23 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$1$ |
$1$ |
|
$1$ |
$640$ |
$0.005938$ |
$5545233/161$ |
$[1, -1, 0, -92, -309]$ |
\(y^2+xy=x^3-x^2-92x-309\) |
4025.e4 |
4025a4 |
4025.e |
4025a |
$4$ |
$4$ |
\( 5^{2} \cdot 7 \cdot 23 \) |
\( - 5^{6} \cdot 7 \cdot 23^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$1$ |
$1$ |
|
$0$ |
$2560$ |
$0.699085$ |
$2014698447/1958887$ |
$[1, -1, 0, 658, 5191]$ |
\(y^2+xy=x^3-x^2+658x+5191\) |
4025.f1 |
4025c4 |
4025.f |
4025c |
$4$ |
$4$ |
\( 5^{2} \cdot 7 \cdot 23 \) |
\( 5^{14} \cdot 7^{3} \cdot 23 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$1$ |
$1$ |
|
$0$ |
$34560$ |
$1.976631$ |
$8244966675515989329/3081640625$ |
$[1, -1, 0, -1052192, 415686091]$ |
\(y^2+xy=x^3-x^2-1052192x+415686091\) |
4025.f2 |
4025c3 |
4025.f |
4025c |
$4$ |
$4$ |
\( 5^{2} \cdot 7 \cdot 23 \) |
\( 5^{8} \cdot 7^{12} \cdot 23 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$1$ |
$1$ |
|
$0$ |
$34560$ |
$1.976631$ |
$18577831198352049/7958740140575$ |
$[1, -1, 0, -137942, -10015159]$ |
\(y^2+xy=x^3-x^2-137942x-10015159\) |
4025.f3 |
4025c2 |
4025.f |
4025c |
$4$ |
$4$ |
\( 5^{2} \cdot 7 \cdot 23 \) |
\( 5^{10} \cdot 7^{6} \cdot 23^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.6.0.1 |
2Cs |
$1$ |
$1$ |
|
$2$ |
$17280$ |
$1.630058$ |
$2041085246738049/38897700625$ |
$[1, -1, 0, -66067, 6444216]$ |
\(y^2+xy=x^3-x^2-66067x+6444216\) |
4025.f4 |
4025c1 |
4025.f |
4025c |
$4$ |
$4$ |
\( 5^{2} \cdot 7 \cdot 23 \) |
\( - 5^{8} \cdot 7^{3} \cdot 23^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$1$ |
$1$ |
|
$1$ |
$8640$ |
$1.283484$ |
$1367631/2399636575$ |
$[1, -1, 0, 58, 294591]$ |
\(y^2+xy=x^3-x^2+58x+294591\) |
4025.g1 |
4025b1 |
4025.g |
4025b |
$2$ |
$2$ |
\( 5^{2} \cdot 7 \cdot 23 \) |
\( 5^{8} \cdot 7^{3} \cdot 23 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$1$ |
$1$ |
|
$1$ |
$3456$ |
$0.782702$ |
$476196576129/197225$ |
$[1, -1, 0, -4067, -98784]$ |
\(y^2+xy=x^3-x^2-4067x-98784\) |
4025.g2 |
4025b2 |
4025.g |
4025b |
$2$ |
$2$ |
\( 5^{2} \cdot 7 \cdot 23 \) |
\( - 5^{7} \cdot 7^{6} \cdot 23^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$1$ |
$1$ |
|
$0$ |
$6912$ |
$1.129276$ |
$-288673724529/311181605$ |
$[1, -1, 0, -3442, -130659]$ |
\(y^2+xy=x^3-x^2-3442x-130659\) |