| 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 |
| 67335.a1 |
67335c1 |
67335.a |
67335c |
$1$ |
$1$ |
\( 3 \cdot 5 \cdot 67^{2} \) |
\( - 3^{10} \cdot 5^{6} \cdot 67^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$134$ |
$2$ |
$0$ |
$1.523271457$ |
$1$ |
|
$4$ |
$342720$ |
$1.523838$ |
$-14018440572928/922640625$ |
$1.01113$ |
$3.86719$ |
$[0, -1, 1, -33656, -2496844]$ |
\(y^2+y=x^3-x^2-33656x-2496844\) |
134.2.0.? |
$[(313, 4187)]$ |
| 67335.b1 |
67335b1 |
67335.b |
67335b |
$1$ |
$1$ |
\( 3 \cdot 5 \cdot 67^{2} \) |
\( - 3 \cdot 5^{6} \cdot 67^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$7.218450548$ |
$1$ |
|
$2$ |
$3449160$ |
$2.446865$ |
$-602927104/46875$ |
$0.88619$ |
$4.85552$ |
$[0, -1, 1, -1303306, -609510144]$ |
\(y^2+y=x^3-x^2-1303306x-609510144\) |
6.2.0.a.1 |
$[(14588, 1756312)]$ |
| 67335.c1 |
67335a1 |
67335.c |
67335a |
$2$ |
$2$ |
\( 3 \cdot 5 \cdot 67^{2} \) |
\( 3^{9} \cdot 5^{2} \cdot 67^{9} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$4020$ |
$12$ |
$0$ |
$6.363633566$ |
$1$ |
|
$3$ |
$14105376$ |
$3.302429$ |
$7532993969227/492075$ |
$1.06601$ |
$6.07087$ |
$[1, 1, 1, -122830356, 523889558244]$ |
\(y^2+xy+y=x^3+x^2-122830356x+523889558244\) |
2.3.0.a.1, 60.6.0.d.1, 402.6.0.?, 1340.6.0.?, 4020.12.0.? |
$[(6339, 2970)]$ |
| 67335.c2 |
67335a2 |
67335.c |
67335a |
$2$ |
$2$ |
\( 3 \cdot 5 \cdot 67^{2} \) |
\( - 3^{18} \cdot 5 \cdot 67^{9} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$4020$ |
$12$ |
$0$ |
$12.72726713$ |
$1$ |
|
$0$ |
$28210752$ |
$3.649002$ |
$-6232551536827/1937102445$ |
$0.98750$ |
$6.09249$ |
$[1, 1, 1, -115311281, 590836394414]$ |
\(y^2+xy+y=x^3+x^2-115311281x+590836394414\) |
2.3.0.a.1, 60.6.0.d.1, 670.6.0.?, 804.6.0.?, 4020.12.0.? |
$[(326119/2, 184391479/2)]$ |
| 67335.d1 |
67335f2 |
67335.d |
67335f |
$2$ |
$2$ |
\( 3 \cdot 5 \cdot 67^{2} \) |
\( 3 \cdot 5^{6} \cdot 67^{9} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$4020$ |
$12$ |
$0$ |
$1$ |
$9$ |
$3$ |
$0$ |
$3389664$ |
$2.769417$ |
$265847707/46875$ |
$0.90279$ |
$5.14873$ |
$[1, 0, 0, -4028971, -2595888760]$ |
\(y^2+xy=x^3-4028971x-2595888760\) |
2.3.0.a.1, 60.6.0.d.1, 402.6.0.?, 1340.6.0.?, 4020.12.0.? |
$[ ]$ |
| 67335.d2 |
67335f1 |
67335.d |
67335f |
$2$ |
$2$ |
\( 3 \cdot 5 \cdot 67^{2} \) |
\( - 3^{2} \cdot 5^{3} \cdot 67^{9} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$4020$ |
$12$ |
$0$ |
$1$ |
$9$ |
$3$ |
$1$ |
$1694832$ |
$2.422844$ |
$456533/1125$ |
$0.85411$ |
$4.68227$ |
$[1, 0, 0, 482474, -232793869]$ |
\(y^2+xy=x^3+482474x-232793869\) |
2.3.0.a.1, 60.6.0.d.1, 670.6.0.?, 804.6.0.?, 4020.12.0.? |
$[ ]$ |
| 67335.e1 |
67335h1 |
67335.e |
67335h |
$2$ |
$2$ |
\( 3 \cdot 5 \cdot 67^{2} \) |
\( 3^{5} \cdot 5^{6} \cdot 67^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$4020$ |
$12$ |
$0$ |
$1.933314959$ |
$1$ |
|
$3$ |
$1615680$ |
$2.455769$ |
$2912566550041/254390625$ |
$0.91283$ |
$4.85078$ |
$[1, 0, 0, -1335571, 547309040]$ |
\(y^2+xy=x^3-1335571x+547309040\) |
2.3.0.a.1, 20.6.0.b.1, 402.6.0.?, 4020.12.0.? |
$[(4796, 320810)]$ |
| 67335.e2 |
67335h2 |
67335.e |
67335h |
$2$ |
$2$ |
\( 3 \cdot 5 \cdot 67^{2} \) |
\( - 3^{10} \cdot 5^{3} \cdot 67^{8} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$4020$ |
$12$ |
$0$ |
$3.866629918$ |
$1$ |
|
$0$ |
$3231360$ |
$2.802341$ |
$3883959939959/33133870125$ |
$0.95785$ |
$5.11237$ |
$[1, 0, 0, 1470054, 2543230665]$ |
\(y^2+xy=x^3+1470054x+2543230665\) |
2.3.0.a.1, 20.6.0.a.1, 804.6.0.?, 4020.12.0.? |
$[(-849/2, 377925/2)]$ |
| 67335.f1 |
67335e2 |
67335.f |
67335e |
$2$ |
$3$ |
\( 3 \cdot 5 \cdot 67^{2} \) |
\( - 3^{4} \cdot 5^{6} \cdot 67^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$402$ |
$16$ |
$0$ |
$1.457623570$ |
$1$ |
|
$4$ |
$6462720$ |
$3.058243$ |
$-2989967081734144/380653171875$ |
$1.01643$ |
$5.49237$ |
$[0, -1, 1, -13472985, 21028830023]$ |
\(y^2+y=x^3-x^2-13472985x+21028830023\) |
3.4.0.a.1, 6.8.0-3.a.1.2, 134.2.0.?, 201.8.0.?, 402.16.0.? |
$[(849, 101002)]$ |
| 67335.f2 |
67335e1 |
67335.f |
67335e |
$2$ |
$3$ |
\( 3 \cdot 5 \cdot 67^{2} \) |
\( - 3^{12} \cdot 5^{2} \cdot 67^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$402$ |
$16$ |
$0$ |
$4.372870710$ |
$1$ |
|
$0$ |
$2154240$ |
$2.508938$ |
$1503484706816/890163675$ |
$1.04611$ |
$4.79130$ |
$[0, -1, 1, 1071375, -65218894]$ |
\(y^2+y=x^3-x^2+1071375x-65218894\) |
3.4.0.a.1, 6.8.0-3.a.1.1, 134.2.0.?, 201.8.0.?, 402.16.0.? |
$[(318765/2, 179986451/2)]$ |
| 67335.g1 |
67335d2 |
67335.g |
67335d |
$2$ |
$2$ |
\( 3 \cdot 5 \cdot 67^{2} \) |
\( 3 \cdot 5^{6} \cdot 67^{3} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$4020$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$50592$ |
$0.667071$ |
$265847707/46875$ |
$0.90279$ |
$2.87949$ |
$[1, 1, 0, -897, 8256]$ |
\(y^2+xy=x^3+x^2-897x+8256\) |
2.3.0.a.1, 60.6.0.d.1, 402.6.0.?, 1340.6.0.?, 4020.12.0.? |
$[ ]$ |
| 67335.g2 |
67335d1 |
67335.g |
67335d |
$2$ |
$2$ |
\( 3 \cdot 5 \cdot 67^{2} \) |
\( - 3^{2} \cdot 5^{3} \cdot 67^{3} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$4020$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$25296$ |
$0.320498$ |
$456533/1125$ |
$0.85411$ |
$2.41303$ |
$[1, 1, 0, 108, 819]$ |
\(y^2+xy=x^3+x^2+108x+819\) |
2.3.0.a.1, 60.6.0.d.1, 670.6.0.?, 804.6.0.?, 4020.12.0.? |
$[ ]$ |
| 67335.h1 |
67335g8 |
67335.h |
67335g |
$8$ |
$16$ |
\( 3 \cdot 5 \cdot 67^{2} \) |
\( 3^{4} \cdot 5 \cdot 67^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.48.0.121 |
2B |
$32160$ |
$768$ |
$13$ |
$12.26408137$ |
$1$ |
|
$0$ |
$1182720$ |
$2.393215$ |
$1114544804970241/405$ |
$1.07354$ |
$5.38572$ |
$[1, 0, 1, -9696334, 11620618247]$ |
\(y^2+xy+y=x^3-9696334x+11620618247\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 10.6.0.a.1, 16.48.0.x.2, $\ldots$ |
$[(42638143/154, -3248058379/154)]$ |
| 67335.h2 |
67335g6 |
67335.h |
67335g |
$8$ |
$16$ |
\( 3 \cdot 5 \cdot 67^{2} \) |
\( 3^{8} \cdot 5^{2} \cdot 67^{6} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.48.0.123 |
2Cs |
$16080$ |
$768$ |
$13$ |
$6.132040686$ |
$1$ |
|
$2$ |
$591360$ |
$2.046642$ |
$272223782641/164025$ |
$1.03897$ |
$4.63758$ |
$[1, 0, 1, -606109, 181479107]$ |
\(y^2+xy+y=x^3-606109x+181479107\) |
2.6.0.a.1, 4.12.0.b.1, 8.48.0.k.1, 20.24.0.c.1, 40.96.1.cc.2, $\ldots$ |
$[(21289/7, 79757/7)]$ |
| 67335.h3 |
67335g7 |
67335.h |
67335g |
$8$ |
$16$ |
\( 3 \cdot 5 \cdot 67^{2} \) |
\( - 3^{16} \cdot 5 \cdot 67^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.48.0.134 |
2B |
$32160$ |
$768$ |
$13$ |
$3.066020343$ |
$1$ |
|
$0$ |
$1182720$ |
$2.393215$ |
$-147281603041/215233605$ |
$1.05949$ |
$4.69566$ |
$[1, 0, 1, -493884, 250789267]$ |
\(y^2+xy+y=x^3-493884x+250789267\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0.ba.2, 16.48.0.u.2, 20.12.0.h.1, $\ldots$ |
$[(61595/2, 15209979/2)]$ |
| 67335.h4 |
67335g4 |
67335.h |
67335g |
$8$ |
$16$ |
\( 3 \cdot 5 \cdot 67^{2} \) |
\( 3 \cdot 5 \cdot 67^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
32.48.0.1 |
2B |
$32160$ |
$768$ |
$13$ |
$49.05632549$ |
$1$ |
|
$0$ |
$295680$ |
$1.700069$ |
$56667352321/15$ |
$1.03019$ |
$4.49642$ |
$[1, 0, 1, -359214, -82896059]$ |
\(y^2+xy+y=x^3-359214x-82896059\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.g.1, 24.24.0.by.2, $\ldots$ |
$[(-41691781849732828157321/10976400162, 233037333142511562484879815997093/10976400162)]$ |
| 67335.h5 |
67335g3 |
67335.h |
67335g |
$8$ |
$16$ |
\( 3 \cdot 5 \cdot 67^{2} \) |
\( 3^{4} \cdot 5^{4} \cdot 67^{6} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.48.0.44 |
2Cs |
$16080$ |
$768$ |
$13$ |
$12.26408137$ |
$1$ |
|
$2$ |
$295680$ |
$1.700069$ |
$111284641/50625$ |
$1.02534$ |
$3.93578$ |
$[1, 0, 1, -44984, 1694657]$ |
\(y^2+xy+y=x^3-44984x+1694657\) |
2.6.0.a.1, 4.24.0.b.1, 8.48.0.b.2, 24.96.1.n.1, 40.96.1.s.1, $\ldots$ |
$[(-1121949/91, 1786643494/91)]$ |
| 67335.h6 |
67335g2 |
67335.h |
67335g |
$8$ |
$16$ |
\( 3 \cdot 5 \cdot 67^{2} \) |
\( 3^{2} \cdot 5^{2} \cdot 67^{6} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.48.0.3 |
2Cs |
$16080$ |
$768$ |
$13$ |
$24.52816274$ |
$1$ |
|
$2$ |
$147840$ |
$1.353495$ |
$13997521/225$ |
$0.96230$ |
$3.74930$ |
$[1, 0, 1, -22539, -1286039]$ |
\(y^2+xy+y=x^3-22539x-1286039\) |
2.6.0.a.1, 4.12.0.b.1, 8.24.0.i.1, 16.48.0.d.2, 24.48.0.bb.2, $\ldots$ |
$[(-98082499759/34489, 6434153624300583/34489)]$ |
| 67335.h7 |
67335g1 |
67335.h |
67335g |
$8$ |
$16$ |
\( 3 \cdot 5 \cdot 67^{2} \) |
\( - 3 \cdot 5 \cdot 67^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
32.48.0.1 |
2B |
$32160$ |
$768$ |
$13$ |
$49.05632549$ |
$1$ |
|
$1$ |
$73920$ |
$1.006922$ |
$-1/15$ |
$1.19808$ |
$3.18337$ |
$[1, 0, 1, -94, -56053]$ |
\(y^2+xy+y=x^3-94x-56053\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.g.1, 24.24.0.bz.1, $\ldots$ |
$[(1820699650548839722503/2817371921, 74905268403088672080439152872684/2817371921)]$ |
| 67335.h8 |
67335g5 |
67335.h |
67335g |
$8$ |
$16$ |
\( 3 \cdot 5 \cdot 67^{2} \) |
\( - 3^{2} \cdot 5^{8} \cdot 67^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.48.0.197 |
2B |
$32160$ |
$768$ |
$13$ |
$24.52816274$ |
$1$ |
|
$0$ |
$591360$ |
$2.046642$ |
$4733169839/3515625$ |
$1.05585$ |
$4.27311$ |
$[1, 0, 1, 157021, 12764531]$ |
\(y^2+xy+y=x^3+157021x+12764531\) |
2.3.0.a.1, 4.12.0.d.1, 8.48.0.n.2, 24.96.1.cv.2, 80.96.1.?, $\ldots$ |
$[(383127971223/63154, 1338047345264198197/63154)]$ |
| 67335.i1 |
67335i1 |
67335.i |
67335i |
$2$ |
$2$ |
\( 3 \cdot 5 \cdot 67^{2} \) |
\( 3^{9} \cdot 5^{2} \cdot 67^{3} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$4020$ |
$12$ |
$0$ |
$3.553518987$ |
$1$ |
|
$1$ |
$210528$ |
$1.200083$ |
$7532993969227/492075$ |
$1.06601$ |
$3.80163$ |
$[1, 0, 1, -27363, -1744319]$ |
\(y^2+xy+y=x^3-27363x-1744319\) |
2.3.0.a.1, 60.6.0.d.1, 402.6.0.?, 1340.6.0.?, 4020.12.0.? |
$[(2903/2, 149049/2)]$ |
| 67335.i2 |
67335i2 |
67335.i |
67335i |
$2$ |
$2$ |
\( 3 \cdot 5 \cdot 67^{2} \) |
\( - 3^{18} \cdot 5 \cdot 67^{3} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$4020$ |
$12$ |
$0$ |
$7.107037975$ |
$1$ |
|
$0$ |
$421056$ |
$1.546656$ |
$-6232551536827/1937102445$ |
$0.98750$ |
$3.82325$ |
$[1, 0, 1, -25688, -1966759]$ |
\(y^2+xy+y=x^3-25688x-1966759\) |
2.3.0.a.1, 60.6.0.d.1, 670.6.0.?, 804.6.0.?, 4020.12.0.? |
$[(21993/8, 2707481/8)]$ |
| 67335.j1 |
67335k1 |
67335.j |
67335k |
$1$ |
$1$ |
\( 3 \cdot 5 \cdot 67^{2} \) |
\( - 3 \cdot 5^{6} \cdot 67^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$51480$ |
$0.344517$ |
$-602927104/46875$ |
$0.88619$ |
$2.58628$ |
$[0, 1, 1, -290, 1931]$ |
\(y^2+y=x^3+x^2-290x+1931\) |
6.2.0.a.1 |
$[ ]$ |
| 67335.k1 |
67335j1 |
67335.k |
67335j |
$1$ |
$1$ |
\( 3 \cdot 5 \cdot 67^{2} \) |
\( - 3^{10} \cdot 5^{6} \cdot 67^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$134$ |
$2$ |
$0$ |
$2.295948485$ |
$1$ |
|
$0$ |
$22962240$ |
$3.626183$ |
$-14018440572928/922640625$ |
$1.01113$ |
$6.13643$ |
$[0, 1, 1, -151083280, 754282037809]$ |
\(y^2+y=x^3+x^2-151083280x+754282037809\) |
134.2.0.? |
$[(-7483/2, 8120597/2)]$ |
