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 |
7098.g1 |
7098f1 |
7098.g |
7098f |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 7 \cdot 13^{2} \) |
\( 2 \cdot 3^{7} \cdot 7^{5} \cdot 13^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$168$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$131040$ |
$1.925154$ |
$249395415529/73513818$ |
$[1, 1, 0, -122528, 11512350]$ |
\(y^2+xy=x^3+x^2-122528x+11512350\) |
168.2.0.? |
$[]$ |
7098.q1 |
7098s1 |
7098.q |
7098s |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 7 \cdot 13^{2} \) |
\( 2 \cdot 3^{7} \cdot 7^{5} \cdot 13^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$168$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$10080$ |
$0.642679$ |
$249395415529/73513818$ |
$[1, 1, 1, -725, 4961]$ |
\(y^2+xy+y=x^3+x^2-725x+4961\) |
168.2.0.? |
$[]$ |
21294.bi1 |
21294x1 |
21294.bi |
21294x |
$1$ |
$1$ |
\( 2 \cdot 3^{2} \cdot 7 \cdot 13^{2} \) |
\( 2 \cdot 3^{13} \cdot 7^{5} \cdot 13^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$168$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$80640$ |
$1.191984$ |
$249395415529/73513818$ |
$[1, -1, 0, -6525, -140477]$ |
\(y^2+xy=x^3-x^2-6525x-140477\) |
168.2.0.? |
$[]$ |
21294.bp1 |
21294ct1 |
21294.bp |
21294ct |
$1$ |
$1$ |
\( 2 \cdot 3^{2} \cdot 7 \cdot 13^{2} \) |
\( 2 \cdot 3^{13} \cdot 7^{5} \cdot 13^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$168$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1048320$ |
$2.474461$ |
$249395415529/73513818$ |
$[1, -1, 1, -1102757, -311936205]$ |
\(y^2+xy+y=x^3-x^2-1102757x-311936205\) |
168.2.0.? |
$[]$ |
49686.y1 |
49686br1 |
49686.y |
49686br |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2 \cdot 3^{7} \cdot 7^{11} \cdot 13^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$168$ |
$2$ |
$0$ |
$0.837561244$ |
$1$ |
|
$4$ |
$6289920$ |
$2.898109$ |
$249395415529/73513818$ |
$[1, 0, 1, -6003898, -3966747718]$ |
\(y^2+xy+y=x^3-6003898x-3966747718\) |
168.2.0.? |
$[(-1676, 38102)]$ |
49686.dl1 |
49686dj1 |
49686.dl |
49686dj |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2 \cdot 3^{7} \cdot 7^{11} \cdot 13^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$168$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$483840$ |
$1.615633$ |
$249395415529/73513818$ |
$[1, 0, 0, -35526, -1808262]$ |
\(y^2+xy=x^3-35526x-1808262\) |
168.2.0.? |
$[]$ |
56784.bq1 |
56784dc1 |
56784.bq |
56784dc |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 13^{2} \) |
\( 2^{13} \cdot 3^{7} \cdot 7^{5} \cdot 13^{2} \) |
$2$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$168$ |
$2$ |
$0$ |
$0.144686178$ |
$1$ |
|
$30$ |
$241920$ |
$1.335827$ |
$249395415529/73513818$ |
$[0, 1, 0, -11600, -340716]$ |
\(y^2=x^3+x^2-11600x-340716\) |
168.2.0.? |
$[(250, 3528), (-44, 294)]$ |
56784.de1 |
56784cs1 |
56784.de |
56784cs |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 13^{2} \) |
\( 2^{13} \cdot 3^{7} \cdot 7^{5} \cdot 13^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$168$ |
$2$ |
$0$ |
$5.627157285$ |
$1$ |
|
$2$ |
$3144960$ |
$2.618301$ |
$249395415529/73513818$ |
$[0, 1, 0, -1960456, -740711308]$ |
\(y^2=x^3+x^2-1960456x-740711308\) |
168.2.0.? |
$[(-877, 17460)]$ |
149058.b1 |
149058ei1 |
149058.b |
149058ei |
$1$ |
$1$ |
\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 13^{2} \) |
\( 2 \cdot 3^{13} \cdot 7^{11} \cdot 13^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$168$ |
$2$ |
$0$ |
$1.151007700$ |
$1$ |
|
$4$ |
$3870720$ |
$2.164940$ |
$249395415529/73513818$ |
$[1, -1, 0, -319734, 48823074]$ |
\(y^2+xy=x^3-x^2-319734x+48823074\) |
168.2.0.? |
$[(-285, 10947)]$ |
149058.io1 |
149058cr1 |
149058.io |
149058cr |
$1$ |
$1$ |
\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 13^{2} \) |
\( 2 \cdot 3^{13} \cdot 7^{11} \cdot 13^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$168$ |
$2$ |
$0$ |
$1$ |
$9$ |
$3$ |
$0$ |
$50319360$ |
$3.447414$ |
$249395415529/73513818$ |
$[1, -1, 1, -54035078, 107102188379]$ |
\(y^2+xy+y=x^3-x^2-54035078x+107102188379\) |
168.2.0.? |
$[]$ |
170352.a1 |
170352b1 |
170352.a |
170352b |
$1$ |
$1$ |
\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{13} \cdot 3^{13} \cdot 7^{5} \cdot 13^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$168$ |
$2$ |
$0$ |
$6.363018181$ |
$1$ |
|
$2$ |
$25159680$ |
$3.167606$ |
$249395415529/73513818$ |
$[0, 0, 0, -17644107, 19981561210]$ |
\(y^2=x^3-17644107x+19981561210\) |
168.2.0.? |
$[(7277, 526248)]$ |
170352.gn1 |
170352cw1 |
170352.gn |
170352cw |
$1$ |
$1$ |
\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 13^{2} \) |
\( 2^{13} \cdot 3^{13} \cdot 7^{5} \cdot 13^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$168$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1935360$ |
$1.885132$ |
$249395415529/73513818$ |
$[0, 0, 0, -104403, 9094930]$ |
\(y^2=x^3-104403x+9094930\) |
168.2.0.? |
$[]$ |
177450.ev1 |
177450gy1 |
177450.ev |
177450gy |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13^{2} \) |
\( 2 \cdot 3^{7} \cdot 5^{6} \cdot 7^{5} \cdot 13^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$168$ |
$2$ |
$0$ |
$0.206219240$ |
$1$ |
|
$6$ |
$806400$ |
$1.447397$ |
$249395415529/73513818$ |
$[1, 0, 1, -18126, 656398]$ |
\(y^2+xy+y=x^3-18126x+656398\) |
168.2.0.? |
$[(2, 786)]$ |
177450.ih1 |
177450bp1 |
177450.ih |
177450bp |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13^{2} \) |
\( 2 \cdot 3^{7} \cdot 5^{6} \cdot 7^{5} \cdot 13^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$168$ |
$2$ |
$0$ |
$2.188902860$ |
$1$ |
|
$0$ |
$10483200$ |
$2.729874$ |
$249395415529/73513818$ |
$[1, 0, 0, -3063213, 1445170167]$ |
\(y^2+xy=x^3-3063213x+1445170167\) |
168.2.0.? |
$[(-2817/2, 459117/2)]$ |
227136.a1 |
227136ch1 |
227136.a |
227136ch |
$1$ |
$1$ |
\( 2^{6} \cdot 3 \cdot 7 \cdot 13^{2} \) |
\( 2^{19} \cdot 3^{7} \cdot 7^{5} \cdot 13^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$168$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$25159680$ |
$2.964874$ |
$249395415529/73513818$ |
$[0, -1, 0, -7841825, -5917848639]$ |
\(y^2=x^3-x^2-7841825x-5917848639\) |
168.2.0.? |
$[]$ |
227136.es1 |
227136ek1 |
227136.es |
227136ek |
$1$ |
$1$ |
\( 2^{6} \cdot 3 \cdot 7 \cdot 13^{2} \) |
\( 2^{19} \cdot 3^{7} \cdot 7^{5} \cdot 13^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$168$ |
$2$ |
$0$ |
$2.986106963$ |
$1$ |
|
$2$ |
$1935360$ |
$1.682400$ |
$249395415529/73513818$ |
$[0, -1, 0, -46401, -2679327]$ |
\(y^2=x^3-x^2-46401x-2679327\) |
168.2.0.? |
$[(-73, 560)]$ |
227136.ew1 |
227136eo1 |
227136.ew |
227136eo |
$1$ |
$1$ |
\( 2^{6} \cdot 3 \cdot 7 \cdot 13^{2} \) |
\( 2^{19} \cdot 3^{7} \cdot 7^{5} \cdot 13^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$168$ |
$2$ |
$0$ |
$0.154423703$ |
$1$ |
|
$8$ |
$25159680$ |
$2.964874$ |
$249395415529/73513818$ |
$[0, 1, 0, -7841825, 5917848639]$ |
\(y^2=x^3+x^2-7841825x+5917848639\) |
168.2.0.? |
$[(-2141, 113568)]$ |
227136.jh1 |
227136gy1 |
227136.jh |
227136gy |
$1$ |
$1$ |
\( 2^{6} \cdot 3 \cdot 7 \cdot 13^{2} \) |
\( 2^{19} \cdot 3^{7} \cdot 7^{5} \cdot 13^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$168$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1935360$ |
$1.682400$ |
$249395415529/73513818$ |
$[0, 1, 0, -46401, 2679327]$ |
\(y^2=x^3+x^2-46401x+2679327\) |
168.2.0.? |
$[]$ |
397488.g1 |
397488g1 |
397488.g |
397488g |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{13} \cdot 3^{7} \cdot 7^{11} \cdot 13^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$168$ |
$2$ |
$0$ |
$2.629535321$ |
$1$ |
|
$0$ |
$150958080$ |
$3.591255$ |
$249395415529/73513818$ |
$[0, -1, 0, -96062360, 253871853936]$ |
\(y^2=x^3-x^2-96062360x+253871853936\) |
168.2.0.? |
$[(11437/2, 405769/2)]$ |
397488.ex1 |
397488ex1 |
397488.ex |
397488ex |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 13^{2} \) |
\( 2^{13} \cdot 3^{7} \cdot 7^{11} \cdot 13^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$168$ |
$2$ |
$0$ |
$5.092380195$ |
$1$ |
|
$2$ |
$11612160$ |
$2.308781$ |
$249395415529/73513818$ |
$[0, -1, 0, -568416, 115728768]$ |
\(y^2=x^3-x^2-568416x+115728768\) |
168.2.0.? |
$[(632, 2920)]$ |