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 |
7728.a1 |
7728j2 |
7728.a |
7728j |
$2$ |
$3$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( - 2^{13} \cdot 3 \cdot 7^{3} \cdot 23^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$0.247697064$ |
$1$ |
|
$8$ |
$8640$ |
$0.794747$ |
$-2181825073/25039686$ |
$[0, -1, 0, -432, 15936]$ |
\(y^2=x^3-x^2-432x+15936\) |
7728.a2 |
7728j1 |
7728.a |
7728j |
$2$ |
$3$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( - 2^{15} \cdot 3^{3} \cdot 7 \cdot 23 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$0.743091192$ |
$1$ |
|
$4$ |
$2880$ |
$0.245441$ |
$2924207/34776$ |
$[0, -1, 0, 48, -576]$ |
\(y^2=x^3-x^2+48x-576\) |
7728.b1 |
7728l4 |
7728.b |
7728l |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( 2^{13} \cdot 3^{6} \cdot 7^{4} \cdot 23 \) |
$1$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.7 |
2B |
$5.617580568$ |
$1$ |
|
$5$ |
$92160$ |
$2.070137$ |
$632678989847546725777/80515134$ |
$[0, -1, 0, -2861584, 1864147264]$ |
\(y^2=x^3-x^2-2861584x+1864147264\) |
7728.b2 |
7728l3 |
7728.b |
7728l |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( 2^{13} \cdot 3^{24} \cdot 7 \cdot 23 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.6 |
2B |
$5.617580568$ |
$1$ |
|
$3$ |
$92160$ |
$2.070137$ |
$231331938231569617/90942310746882$ |
$[0, -1, 0, -204624, 20243520]$ |
\(y^2=x^3-x^2-204624x+20243520\) |
7728.b3 |
7728l2 |
7728.b |
7728l |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( 2^{14} \cdot 3^{12} \cdot 7^{2} \cdot 23^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.1 |
2Cs |
$2.808790284$ |
$1$ |
|
$9$ |
$46080$ |
$1.723562$ |
$154502321244119857/55101928644$ |
$[0, -1, 0, -178864, 29166784]$ |
\(y^2=x^3-x^2-178864x+29166784\) |
7728.b4 |
7728l1 |
7728.b |
7728l |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( - 2^{16} \cdot 3^{6} \cdot 7 \cdot 23^{4} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.8 |
2B |
$1.404395142$ |
$1$ |
|
$7$ |
$23040$ |
$1.376987$ |
$-23771111713777/22848457968$ |
$[0, -1, 0, -9584, 592320]$ |
\(y^2=x^3-x^2-9584x+592320\) |
7728.c1 |
7728h4 |
7728.c |
7728h |
$4$ |
$6$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( 2^{27} \cdot 3^{2} \cdot 7^{12} \cdot 23^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.6, 3.4.0.1 |
2B, 3B |
$1$ |
$1$ |
|
$1$ |
$691200$ |
$3.053509$ |
$385693937170561837203625/2159357734550274048$ |
$[0, -1, 0, -24263848, 45788177008]$ |
\(y^2=x^3-x^2-24263848x+45788177008\) |
7728.c2 |
7728h2 |
7728.c |
7728h |
$4$ |
$6$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( 2^{17} \cdot 3^{6} \cdot 7^{4} \cdot 23^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.6, 3.4.0.1 |
2B, 3B |
$1$ |
$1$ |
|
$1$ |
$230400$ |
$2.504204$ |
$155355156733986861625/8291568305839392$ |
$[0, -1, 0, -1791928, -879068816]$ |
\(y^2=x^3-x^2-1791928x-879068816\) |
7728.c3 |
7728h3 |
7728.c |
7728h |
$4$ |
$6$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( - 2^{42} \cdot 3^{4} \cdot 7^{6} \cdot 23 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.1, 3.4.0.1 |
2B, 3B |
$1$ |
$1$ |
|
$1$ |
$345600$ |
$2.706936$ |
$-8152944444844179625/235342826399858688$ |
$[0, -1, 0, -670888, 1508909680]$ |
\(y^2=x^3-x^2-670888x+1508909680\) |
7728.c4 |
7728h1 |
7728.c |
7728h |
$4$ |
$6$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( - 2^{22} \cdot 3^{12} \cdot 7^{2} \cdot 23^{3} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.1, 3.4.0.1 |
2B, 3B |
$1$ |
$1$ |
|
$1$ |
$115200$ |
$2.157631$ |
$11079872671250375/324440155855872$ |
$[0, -1, 0, 74312, -54937232]$ |
\(y^2=x^3-x^2+74312x-54937232\) |
7728.d1 |
7728i1 |
7728.d |
7728i |
$2$ |
$3$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( - 2^{8} \cdot 3^{15} \cdot 7 \cdot 23^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$6.047072195$ |
$1$ |
|
$2$ |
$47520$ |
$1.888161$ |
$-47327266415721472000/1222082060283$ |
$[0, -1, 0, -478493, -127241151]$ |
\(y^2=x^3-x^2-478493x-127241151\) |
7728.d2 |
7728i2 |
7728.d |
7728i |
$2$ |
$3$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( - 2^{8} \cdot 3^{5} \cdot 7^{3} \cdot 23^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$2.015690731$ |
$1$ |
|
$2$ |
$142560$ |
$2.437466$ |
$-1400832679220224000/150124273180279587$ |
$[0, -1, 0, -148013, -299020767]$ |
\(y^2=x^3-x^2-148013x-299020767\) |
7728.e1 |
7728g1 |
7728.e |
7728g |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( - 2^{12} \cdot 3 \cdot 7 \cdot 23 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$800$ |
$-0.104682$ |
$512000/483$ |
$[0, -1, 0, 27, -51]$ |
\(y^2=x^3-x^2+27x-51\) |
7728.f1 |
7728d1 |
7728.f |
7728d |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( - 2^{8} \cdot 3^{7} \cdot 7 \cdot 23 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$2240$ |
$0.205352$ |
$128000/352107$ |
$[0, -1, 0, 7, -459]$ |
\(y^2=x^3-x^2+7x-459\) |
7728.g1 |
7728k2 |
7728.g |
7728k |
$2$ |
$2$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( 2^{15} \cdot 3^{2} \cdot 7^{4} \cdot 23^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.6 |
2B |
$0.838575060$ |
$1$ |
|
$7$ |
$9216$ |
$1.016993$ |
$5182207647625/91449288$ |
$[0, -1, 0, -5768, -164112]$ |
\(y^2=x^3-x^2-5768x-164112\) |
7728.g2 |
7728k1 |
7728.g |
7728k |
$2$ |
$2$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( - 2^{18} \cdot 3^{4} \cdot 7^{2} \cdot 23 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.1 |
2B |
$1.677150120$ |
$1$ |
|
$5$ |
$4608$ |
$0.670420$ |
$-15625/5842368$ |
$[0, -1, 0, -8, -7440]$ |
\(y^2=x^3-x^2-8x-7440\) |
7728.h1 |
7728a2 |
7728.h |
7728a |
$2$ |
$2$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( 2^{11} \cdot 3^{8} \cdot 7^{2} \cdot 23 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$1.682013834$ |
$1$ |
|
$5$ |
$5120$ |
$0.660947$ |
$26860713266/7394247$ |
$[0, -1, 0, -792, 6480]$ |
\(y^2=x^3-x^2-792x+6480\) |
7728.h2 |
7728a1 |
7728.h |
7728a |
$2$ |
$2$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( - 2^{10} \cdot 3^{4} \cdot 7 \cdot 23^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$0.841006917$ |
$1$ |
|
$7$ |
$2560$ |
$0.314373$ |
$224727548/299943$ |
$[0, -1, 0, 128, 592]$ |
\(y^2=x^3-x^2+128x+592\) |
7728.i1 |
7728b4 |
7728.i |
7728b |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( 2^{11} \cdot 3^{2} \cdot 7^{2} \cdot 23^{4} \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.49 |
2B |
$1$ |
$1$ |
|
$3$ |
$16384$ |
$1.160669$ |
$369937818893666/123409881$ |
$[0, -1, 0, -18992, 1013472]$ |
\(y^2=x^3-x^2-18992x+1013472\) |
7728.i2 |
7728b3 |
7728.i |
7728b |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( 2^{11} \cdot 3^{2} \cdot 7^{8} \cdot 23 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.101 |
2B |
$1$ |
$1$ |
|
$1$ |
$16384$ |
$1.160669$ |
$48260105780546/1193313807$ |
$[0, -1, 0, -9632, -352800]$ |
\(y^2=x^3-x^2-9632x-352800\) |
7728.i3 |
7728b2 |
7728.i |
7728b |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( 2^{10} \cdot 3^{4} \cdot 7^{4} \cdot 23^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.2 |
2Cs |
$1$ |
$1$ |
|
$3$ |
$8192$ |
$0.814096$ |
$267100692772/102880449$ |
$[0, -1, 0, -1352, 11520]$ |
\(y^2=x^3-x^2-1352x+11520\) |
7728.i4 |
7728b1 |
7728.i |
7728b |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( - 2^{8} \cdot 3^{8} \cdot 7^{2} \cdot 23 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.60 |
2B |
$1$ |
$1$ |
|
$1$ |
$4096$ |
$0.467523$ |
$8284506032/7394247$ |
$[0, -1, 0, 268, 1152]$ |
\(y^2=x^3-x^2+268x+1152\) |
7728.j1 |
7728m1 |
7728.j |
7728m |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( - 2^{21} \cdot 3 \cdot 7^{11} \cdot 23 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$0.562420442$ |
$1$ |
|
$4$ |
$95040$ |
$2.037277$ |
$83228502970940543/69854999176704$ |
$[0, -1, 0, 145536, -14389248]$ |
\(y^2=x^3-x^2+145536x-14389248\) |
7728.k1 |
7728c1 |
7728.k |
7728c |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( - 2^{8} \cdot 3 \cdot 7^{3} \cdot 23 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$3264$ |
$0.136544$ |
$-3525581824/23667$ |
$[0, -1, 0, -201, 1173]$ |
\(y^2=x^3-x^2-201x+1173\) |
7728.l1 |
7728n1 |
7728.l |
7728n |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( - 2^{12} \cdot 3^{5} \cdot 7 \cdot 23^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$12000$ |
$0.818668$ |
$-98867482624/20696067$ |
$[0, -1, 0, -1541, 27693]$ |
\(y^2=x^3-x^2-1541x+27693\) |
7728.m1 |
7728q2 |
7728.m |
7728q |
$2$ |
$2$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( 2^{13} \cdot 3^{2} \cdot 7^{4} \cdot 23^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.6 |
2B |
$0.986172238$ |
$1$ |
|
$7$ |
$9216$ |
$0.796187$ |
$42180533641/22862322$ |
$[0, 1, 0, -1160, 3444]$ |
\(y^2=x^3+x^2-1160x+3444\) |
7728.m2 |
7728q1 |
7728.m |
7728q |
$2$ |
$2$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( - 2^{14} \cdot 3^{4} \cdot 7^{2} \cdot 23 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.1 |
2B |
$0.493086119$ |
$1$ |
|
$11$ |
$4608$ |
$0.449614$ |
$590589719/365148$ |
$[0, 1, 0, 280, 564]$ |
\(y^2=x^3+x^2+280x+564\) |
7728.n1 |
7728f1 |
7728.n |
7728f |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( - 2^{11} \cdot 3^{5} \cdot 7^{3} \cdot 23 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$0.054504924$ |
$1$ |
|
$14$ |
$4800$ |
$0.543468$ |
$-3261064466/1917027$ |
$[0, 1, 0, -392, 4116]$ |
\(y^2=x^3+x^2-392x+4116\) |
7728.o1 |
7728r5 |
7728.o |
7728r |
$6$ |
$8$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( 2^{14} \cdot 3^{16} \cdot 7 \cdot 23^{2} \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.48.0.32 |
2B |
$1$ |
$1$ |
|
$3$ |
$98304$ |
$2.109123$ |
$54804145548726848737/637608031452$ |
$[0, 1, 0, -1266144, 547941492]$ |
\(y^2=x^3+x^2-1266144x+547941492\) |
7728.o2 |
7728r3 |
7728.o |
7728r |
$6$ |
$8$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( 2^{16} \cdot 3^{2} \cdot 7^{8} \cdot 23 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.48.0.176 |
2B |
$1$ |
$4$ |
$2$ |
$1$ |
$49152$ |
$1.762548$ |
$614716917569296417/19093020912$ |
$[0, 1, 0, -283424, -58169868]$ |
\(y^2=x^3+x^2-283424x-58169868\) |
7728.o3 |
7728r4 |
7728.o |
7728r |
$6$ |
$8$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( 2^{16} \cdot 3^{8} \cdot 7^{2} \cdot 23^{4} \) |
$0$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.48.0.25 |
2Cs |
$1$ |
$1$ |
|
$7$ |
$49152$ |
$1.762548$ |
$14447092394873377/1439452851984$ |
$[0, 1, 0, -81184, 8073716]$ |
\(y^2=x^3+x^2-81184x+8073716\) |
7728.o4 |
7728r2 |
7728.o |
7728r |
$6$ |
$8$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( 2^{20} \cdot 3^{4} \cdot 7^{4} \cdot 23^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.48.0.32 |
2Cs |
$1$ |
$1$ |
|
$3$ |
$24576$ |
$1.415974$ |
$169967019783457/26337394944$ |
$[0, 1, 0, -18464, -832524]$ |
\(y^2=x^3+x^2-18464x-832524\) |
7728.o5 |
7728r1 |
7728.o |
7728r |
$6$ |
$8$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( - 2^{28} \cdot 3^{2} \cdot 7^{2} \cdot 23 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.48.0.43 |
2B |
$1$ |
$1$ |
|
$1$ |
$12288$ |
$1.069401$ |
$221115865823/664731648$ |
$[0, 1, 0, 2016, -70668]$ |
\(y^2=x^3+x^2+2016x-70668\) |
7728.o6 |
7728r6 |
7728.o |
7728r |
$6$ |
$8$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( - 2^{14} \cdot 3^{4} \cdot 7 \cdot 23^{8} \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.48.0.161 |
2B |
$1$ |
$1$ |
|
$3$ |
$98304$ |
$2.109123$ |
$27207619911317663/177609314617308$ |
$[0, 1, 0, 100256, 39208820]$ |
\(y^2=x^3+x^2+100256x+39208820\) |
7728.p1 |
7728u2 |
7728.p |
7728u |
$2$ |
$2$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( 2^{17} \cdot 3^{8} \cdot 7^{6} \cdot 23 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$0.308634101$ |
$1$ |
|
$11$ |
$46080$ |
$1.675484$ |
$4144806984356137/568114785504$ |
$[0, 1, 0, -53544, -4183884]$ |
\(y^2=x^3+x^2-53544x-4183884\) |
7728.p2 |
7728u1 |
7728.p |
7728u |
$2$ |
$2$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( - 2^{22} \cdot 3^{4} \cdot 7^{3} \cdot 23^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$0.617268203$ |
$1$ |
|
$9$ |
$23040$ |
$1.328909$ |
$4101378352343/15049939968$ |
$[0, 1, 0, 5336, -344908]$ |
\(y^2=x^3+x^2+5336x-344908\) |
7728.q1 |
7728e2 |
7728.q |
7728e |
$2$ |
$2$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( 2^{11} \cdot 3^{6} \cdot 7^{4} \cdot 23^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.6 |
2B |
$0.129664739$ |
$1$ |
|
$15$ |
$21504$ |
$1.300497$ |
$1566789944863250/925924041$ |
$[0, 1, 0, -30728, 2061972]$ |
\(y^2=x^3+x^2-30728x+2061972\) |
7728.q2 |
7728e1 |
7728.q |
7728e |
$2$ |
$2$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( - 2^{10} \cdot 3^{12} \cdot 7^{2} \cdot 23 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.1 |
2B |
$0.259329478$ |
$1$ |
|
$13$ |
$10752$ |
$0.953924$ |
$-416618810500/598934007$ |
$[0, 1, 0, -1568, 44100]$ |
\(y^2=x^3+x^2-1568x+44100\) |
7728.r1 |
7728t1 |
7728.r |
7728t |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( - 2^{8} \cdot 3^{5} \cdot 7^{5} \cdot 23 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$0.207116622$ |
$1$ |
|
$6$ |
$7200$ |
$0.673561$ |
$-7023616000/93934323$ |
$[0, 1, 0, -253, -7705]$ |
\(y^2=x^3+x^2-253x-7705\) |
7728.s1 |
7728o1 |
7728.s |
7728o |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( - 2^{17} \cdot 3^{9} \cdot 7 \cdot 23 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$0.153035381$ |
$1$ |
|
$8$ |
$8640$ |
$1.086926$ |
$-25727239787761/101406816$ |
$[0, 1, 0, -9840, 373716]$ |
\(y^2=x^3+x^2-9840x+373716\) |
7728.t1 |
7728p2 |
7728.t |
7728p |
$2$ |
$2$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( 2^{23} \cdot 3^{16} \cdot 7^{2} \cdot 23 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$1.644099715$ |
$1$ |
|
$3$ |
$202752$ |
$2.442631$ |
$1733490909744055732873/99355964553216$ |
$[0, 1, 0, -4004232, -3085271820]$ |
\(y^2=x^3+x^2-4004232x-3085271820\) |
7728.t2 |
7728p1 |
7728.t |
7728p |
$2$ |
$2$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( - 2^{34} \cdot 3^{8} \cdot 7 \cdot 23^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$3.288199430$ |
$1$ |
|
$3$ |
$101376$ |
$2.096054$ |
$-354499561600764553/101902222098432$ |
$[0, 1, 0, -235912, -54035212]$ |
\(y^2=x^3+x^2-235912x-54035212\) |
7728.u1 |
7728s1 |
7728.u |
7728s |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
\( - 2^{25} \cdot 3^{3} \cdot 7^{5} \cdot 23 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$37440$ |
$1.632549$ |
$-14943832855786297/85501108224$ |
$[0, 1, 0, -82104, 9072468]$ |
\(y^2=x^3+x^2-82104x+9072468\) |