| 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 |
| 7803.a1 |
7803i1 |
7803.a |
7803i |
$1$ |
$1$ |
\( 3^{3} \cdot 17^{2} \) |
\( - 3^{3} \cdot 17^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$102$ |
$2$ |
$0$ |
$1.743184308$ |
$1$ |
|
$2$ |
$19008$ |
$0.980433$ |
$-242970624/17$ |
$1.34713$ |
$4.41894$ |
$[0, 0, 1, -11271, -460594]$ |
\(y^2+y=x^3-11271x-460594\) |
102.2.0.? |
$[(136, 722)]$ |
| 7803.b1 |
7803h1 |
7803.b |
7803h |
$1$ |
$1$ |
\( 3^{3} \cdot 17^{2} \) |
\( - 3^{3} \cdot 17^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
|
$6$ |
$2$ |
$0$ |
$0.403757772$ |
$1$ |
|
$4$ |
$864$ |
$-0.303401$ |
$-1880064$ |
$0.99575$ |
$2.61206$ |
$[0, 0, 1, -51, 140]$ |
\(y^2+y=x^3-51x+140\) |
6.2.0.a.1 |
$[(4, 0)]$ |
| 7803.c1 |
7803u1 |
7803.c |
7803u |
$1$ |
$1$ |
\( 3^{3} \cdot 17^{2} \) |
\( - 3^{3} \cdot 17^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
|
$6$ |
$2$ |
$0$ |
$0.857879039$ |
$1$ |
|
$0$ |
$14688$ |
$1.113207$ |
$-1880064$ |
$0.99575$ |
$4.50883$ |
$[0, 0, 1, -14739, 689048]$ |
\(y^2+y=x^3-14739x+689048\) |
6.2.0.a.1 |
$[(289/2, 285/2)]$ |
| 7803.d1 |
7803p1 |
7803.d |
7803p |
$1$ |
$1$ |
\( 3^{3} \cdot 17^{2} \) |
\( - 3^{3} \cdot 17^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$17280$ |
$0.847167$ |
$110592/289$ |
$0.90890$ |
$3.70062$ |
$[0, 0, 1, 867, -18424]$ |
\(y^2+y=x^3+867x-18424\) |
6.2.0.a.1 |
$[ ]$ |
| 7803.e1 |
7803m1 |
7803.e |
7803m |
$1$ |
$1$ |
\( 3^{3} \cdot 17^{2} \) |
\( 3^{9} \cdot 17^{10} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
|
$12$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$93636$ |
$1.913822$ |
$7803$ |
$0.90890$ |
$5.26451$ |
$[1, -1, 1, -140942, -17934830]$ |
\(y^2+xy+y=x^3-x^2-140942x-17934830\) |
12.2.0.a.1 |
$[ ]$ |
| 7803.f1 |
7803f1 |
7803.f |
7803f |
$1$ |
$1$ |
\( 3^{3} \cdot 17^{2} \) |
\( - 3^{9} \cdot 17^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$102$ |
$2$ |
$0$ |
$2.074238144$ |
$1$ |
|
$2$ |
$10368$ |
$1.155737$ |
$-27/17$ |
$0.99575$ |
$4.14802$ |
$[1, -1, 1, -488, 136918]$ |
\(y^2+xy+y=x^3-x^2-488x+136918\) |
102.2.0.? |
$[(98, 962)]$ |
| 7803.g1 |
7803j1 |
7803.g |
7803j |
$1$ |
$1$ |
\( 3^{3} \cdot 17^{2} \) |
\( 3^{9} \cdot 17^{4} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
|
$12$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$5508$ |
$0.497216$ |
$7803$ |
$0.90890$ |
$3.36775$ |
$[1, -1, 1, -488, -3536]$ |
\(y^2+xy+y=x^3-x^2-488x-3536\) |
12.2.0.a.1 |
$[ ]$ |
| 7803.h1 |
7803k1 |
7803.h |
7803k |
$2$ |
$3$ |
\( 3^{3} \cdot 17^{2} \) |
\( - 3^{3} \cdot 17^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$102$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$5184$ |
$0.721362$ |
$-884736/17$ |
$0.94133$ |
$3.79601$ |
$[0, 0, 1, -1734, -28250]$ |
\(y^2+y=x^3-1734x-28250\) |
3.4.0.a.1, 6.8.0-3.a.1.1, 51.8.0-3.a.1.1, 102.16.0.? |
$[ ]$ |
| 7803.h2 |
7803k2 |
7803.h |
7803k |
$2$ |
$3$ |
\( 3^{3} \cdot 17^{2} \) |
\( - 3^{5} \cdot 17^{9} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$102$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$15552$ |
$1.270668$ |
$6291456/4913$ |
$1.15047$ |
$4.25641$ |
$[0, 0, 1, 6936, -131423]$ |
\(y^2+y=x^3+6936x-131423\) |
3.4.0.a.1, 6.8.0-3.a.1.2, 51.8.0-3.a.1.2, 102.16.0.? |
$[ ]$ |
| 7803.i1 |
7803c2 |
7803.i |
7803c |
$2$ |
$3$ |
\( 3^{3} \cdot 17^{2} \) |
\( - 3^{9} \cdot 17^{10} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$14.97173826$ |
$1$ |
|
$0$ |
$66096$ |
$1.863853$ |
$0$ |
|
$5.09630$ |
$[0, 0, 1, 0, -9584035]$ |
\(y^2+y=x^3-9584035\) |
|
$[(2055913/86, 2193423511/86)]$ |
| 7803.i2 |
7803c1 |
7803.i |
7803c |
$2$ |
$3$ |
\( 3^{3} \cdot 17^{2} \) |
\( - 3^{3} \cdot 17^{10} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$4.990579421$ |
$1$ |
|
$2$ |
$22032$ |
$1.314547$ |
$0$ |
|
$4.36081$ |
$[0, 0, 1, 0, 354964]$ |
\(y^2+y=x^3+354964\) |
|
$[(86, 995)]$ |
| 7803.j1 |
7803q2 |
7803.j |
7803q |
$2$ |
$3$ |
\( 3^{3} \cdot 17^{2} \) |
\( - 3^{9} \cdot 17^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.648.18.4 |
3B.1.2 |
|
|
|
$3.564428030$ |
$1$ |
|
$2$ |
$16524$ |
$1.391651$ |
$0$ |
|
$4.46404$ |
$[0, 0, 1, 0, -563767]$ |
\(y^2+y=x^3-563767\) |
|
$[(93, 490)]$ |
| 7803.j2 |
7803q1 |
7803.j |
7803q |
$2$ |
$3$ |
\( 3^{3} \cdot 17^{2} \) |
\( - 3^{3} \cdot 17^{8} \) |
$1$ |
$\Z/3\Z$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.648.18.1 |
3B.1.1 |
|
|
|
$10.69328409$ |
$1$ |
|
$2$ |
$5508$ |
$0.842344$ |
$0$ |
|
$3.72855$ |
$[0, 0, 1, 0, 20880]$ |
\(y^2+y=x^3+20880\) |
|
$[(-17910/31, 3560904/31)]$ |
| 7803.k1 |
7803a4 |
7803.k |
7803a |
$4$ |
$27$ |
\( 3^{3} \cdot 17^{2} \) |
\( - 3^{11} \cdot 17^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$12.73716166$ |
$1$ |
|
$0$ |
$15552$ |
$1.468754$ |
$-12288000$ |
$1.23864$ |
$5.06661$ |
$[0, 0, 1, -78030, -8390176]$ |
\(y^2+y=x^3-78030x-8390176\) |
|
$[(3970537/106, 3402396543/106)]$ |
| 7803.k2 |
7803a3 |
7803.k |
7803a |
$4$ |
$27$ |
\( 3^{3} \cdot 17^{2} \) |
\( - 3^{5} \cdot 17^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-27$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$0.471746728$ |
$1$ |
|
$4$ |
$5184$ |
$0.919449$ |
$-12288000$ |
$1.23864$ |
$4.33112$ |
$[0, 0, 1, -8670, 310747]$ |
\(y^2+y=x^3-8670x+310747\) |
|
$[(85, 433)]$ |
| 7803.k3 |
7803a2 |
7803.k |
7803a |
$4$ |
$27$ |
\( 3^{3} \cdot 17^{2} \) |
\( - 3^{9} \cdot 17^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.972.55.16 |
3Cs |
|
|
|
$4.245720553$ |
$1$ |
|
$0$ |
$5184$ |
$0.919449$ |
$0$ |
|
$3.83179$ |
$[0, 0, 1, 0, -33163]$ |
\(y^2+y=x^3-33163\) |
|
$[(1105/2, 36699/2)]$ |
| 7803.k4 |
7803a1 |
7803.k |
7803a |
$4$ |
$27$ |
\( 3^{3} \cdot 17^{2} \) |
\( - 3^{3} \cdot 17^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.972.55.16 |
3Cs |
|
|
|
$1.415240184$ |
$1$ |
|
$0$ |
$1728$ |
$0.370142$ |
$0$ |
|
$3.09630$ |
$[0, 0, 1, 0, 1228]$ |
\(y^2+y=x^3+1228\) |
|
$[(17/2, 285/2)]$ |
| 7803.l1 |
7803b2 |
7803.l |
7803b |
$2$ |
$3$ |
\( 3^{3} \cdot 17^{2} \) |
\( - 3^{9} \cdot 17^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$3.661100789$ |
$1$ |
|
$0$ |
$972$ |
$-0.024956$ |
$0$ |
|
$2.56728$ |
$[0, 0, 1, 0, -115]$ |
\(y^2+y=x^3-115\) |
|
$[(25/2, 87/2)]$ |
| 7803.l2 |
7803b1 |
7803.l |
7803b |
$2$ |
$3$ |
\( 3^{3} \cdot 17^{2} \) |
\( - 3^{3} \cdot 17^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1.220366929$ |
$1$ |
|
$2$ |
$324$ |
$-0.574262$ |
$0$ |
|
$1.83179$ |
$[0, 0, 1, 0, 4]$ |
\(y^2+y=x^3+4\) |
|
$[(2, 3)]$ |
| 7803.m1 |
7803r2 |
7803.m |
7803r |
$2$ |
$3$ |
\( 3^{3} \cdot 17^{2} \) |
\( - 3^{9} \cdot 17^{4} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.648.18.4 |
3B.1.2 |
|
|
|
$1.927294073$ |
$1$ |
|
$2$ |
$3888$ |
$0.447246$ |
$0$ |
|
$3.19954$ |
$[0, 0, 1, 0, -1951]$ |
\(y^2+y=x^3-1951\) |
|
$[(21, 85)]$ |
| 7803.m2 |
7803r1 |
7803.m |
7803r |
$2$ |
$3$ |
\( 3^{3} \cdot 17^{2} \) |
\( - 3^{3} \cdot 17^{4} \) |
$1$ |
$\Z/3\Z$ |
$\Q(\sqrt{-3})$ |
$-3$ |
$N(\mathrm{U}(1))$ |
|
✓ |
$3$ |
27.648.18.1 |
3B.1.1 |
|
|
|
$5.781882221$ |
$1$ |
|
$4$ |
$1296$ |
$-0.102060$ |
$0$ |
|
$2.46404$ |
$[0, 0, 1, 0, 72]$ |
\(y^2+y=x^3+72\) |
|
$[(2142, 99135)]$ |
| 7803.n1 |
7803d1 |
7803.n |
7803d |
$2$ |
$3$ |
\( 3^{3} \cdot 17^{2} \) |
\( - 3^{9} \cdot 17^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$102$ |
$16$ |
$0$ |
$1.329115721$ |
$1$ |
|
$2$ |
$15552$ |
$1.270668$ |
$-884736/17$ |
$0.94133$ |
$4.53150$ |
$[0, 0, 1, -15606, 762743]$ |
\(y^2+y=x^3-15606x+762743\) |
3.4.0.a.1, 6.8.0-3.a.1.2, 51.8.0-3.a.1.2, 102.16.0.? |
$[(-17, 1011)]$ |
| 7803.n2 |
7803d2 |
7803.n |
7803d |
$2$ |
$3$ |
\( 3^{3} \cdot 17^{2} \) |
\( - 3^{11} \cdot 17^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$102$ |
$16$ |
$0$ |
$3.987347163$ |
$1$ |
|
$0$ |
$46656$ |
$1.819975$ |
$6291456/4913$ |
$1.15047$ |
$4.99190$ |
$[0, 0, 1, 62424, 3548414]$ |
\(y^2+y=x^3+62424x+3548414\) |
3.4.0.a.1, 6.8.0-3.a.1.1, 51.8.0-3.a.1.1, 102.16.0.? |
$[(4777/4, 447051/4)]$ |
| 7803.o1 |
7803s1 |
7803.o |
7803s |
$1$ |
$1$ |
\( 3^{3} \cdot 17^{2} \) |
\( 3^{3} \cdot 17^{4} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
|
$12$ |
$2$ |
$0$ |
$0.430182598$ |
$1$ |
|
$2$ |
$1836$ |
$-0.052090$ |
$7803$ |
$0.90890$ |
$2.63225$ |
$[1, -1, 0, -54, 149]$ |
\(y^2+xy=x^3-x^2-54x+149\) |
12.2.0.a.1 |
$[(-4, 19)]$ |
| 7803.p1 |
7803l1 |
7803.p |
7803l |
$1$ |
$1$ |
\( 3^{3} \cdot 17^{2} \) |
\( - 3^{3} \cdot 17^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$102$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$3456$ |
$0.606430$ |
$-27/17$ |
$0.99575$ |
$3.41253$ |
$[1, -1, 0, -54, -5053]$ |
\(y^2+xy=x^3-x^2-54x-5053\) |
102.2.0.? |
$[ ]$ |
| 7803.q1 |
7803e1 |
7803.q |
7803e |
$1$ |
$1$ |
\( 3^{3} \cdot 17^{2} \) |
\( 3^{3} \cdot 17^{10} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
|
$12$ |
$2$ |
$0$ |
$10.56772327$ |
$1$ |
|
$0$ |
$31212$ |
$1.364517$ |
$7803$ |
$0.90890$ |
$4.52902$ |
$[1, -1, 0, -15660, 669473]$ |
\(y^2+xy=x^3-x^2-15660x+669473\) |
12.2.0.a.1 |
$[(-3064/17, 4513379/17)]$ |
| 7803.r1 |
7803o1 |
7803.r |
7803o |
$1$ |
$1$ |
\( 3^{3} \cdot 17^{2} \) |
\( - 3^{9} \cdot 17^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$51840$ |
$1.396473$ |
$110592/289$ |
$0.90890$ |
$4.43611$ |
$[0, 0, 1, 7803, 497441]$ |
\(y^2+y=x^3+7803x+497441\) |
6.2.0.a.1 |
$[ ]$ |
| 7803.s1 |
7803t1 |
7803.s |
7803t |
$1$ |
$1$ |
\( 3^{3} \cdot 17^{2} \) |
\( - 3^{9} \cdot 17^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
|
$6$ |
$2$ |
$0$ |
$19.81667675$ |
$1$ |
|
$0$ |
$44064$ |
$1.662512$ |
$-1880064$ |
$0.99575$ |
$5.24432$ |
$[0, 0, 1, -132651, -18604303]$ |
\(y^2+y=x^3-132651x-18604303\) |
6.2.0.a.1 |
$[(1725767649/322, 71675133238813/322)]$ |
| 7803.t1 |
7803n1 |
7803.t |
7803n |
$1$ |
$1$ |
\( 3^{3} \cdot 17^{2} \) |
\( - 3^{9} \cdot 17^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$102$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$57024$ |
$1.529737$ |
$-242970624/17$ |
$1.34713$ |
$5.15443$ |
$[0, 0, 1, -101439, 12436031]$ |
\(y^2+y=x^3-101439x+12436031\) |
102.2.0.? |
$[ ]$ |
| 7803.u1 |
7803g1 |
7803.u |
7803g |
$1$ |
$1$ |
\( 3^{3} \cdot 17^{2} \) |
\( - 3^{9} \cdot 17^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
|
$6$ |
$2$ |
$0$ |
$17.01262680$ |
$1$ |
|
$0$ |
$2592$ |
$0.245905$ |
$-1880064$ |
$0.99575$ |
$3.34756$ |
$[0, 0, 1, -459, -3787]$ |
\(y^2+y=x^3-459x-3787\) |
6.2.0.a.1 |
$[(22980961/346, 109428529035/346)]$ |
