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 |
966.j3 |
966i2 |
966.j |
966i |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 7 \cdot 23 \) |
\( 2^{2} \cdot 3^{12} \cdot 7^{2} \cdot 23^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
4.12.0.1 |
2Cs |
$1$ |
$1$ |
|
$2$ |
$1920$ |
$1.030415$ |
$154502321244119857/55101928644$ |
$[1, 0, 0, -11179, -455731]$ |
\(y^2+xy=x^3-11179x-455731\) |
2898.f3 |
2898e2 |
2898.f |
2898e |
$4$ |
$4$ |
\( 2 \cdot 3^{2} \cdot 7 \cdot 23 \) |
\( 2^{2} \cdot 3^{18} \cdot 7^{2} \cdot 23^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.6.0.1 |
2Cs |
$1$ |
$1$ |
|
$2$ |
$15360$ |
$1.579721$ |
$154502321244119857/55101928644$ |
$[1, -1, 0, -100611, 12304737]$ |
\(y^2+xy=x^3-x^2-100611x+12304737\) |
6762.bc3 |
6762bb2 |
6762.bc |
6762bb |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 7^{2} \cdot 23 \) |
\( 2^{2} \cdot 3^{12} \cdot 7^{8} \cdot 23^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.1 |
2Cs |
$1$ |
$4$ |
$2$ |
$2$ |
$92160$ |
$2.003368$ |
$154502321244119857/55101928644$ |
$[1, 1, 1, -547772, 155767961]$ |
\(y^2+xy+y=x^3+x^2-547772x+155767961\) |
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 |
$2.808790284$ |
$1$ |
|
$9$ |
$46080$ |
$1.723562$ |
$154502321244119857/55101928644$ |
$[0, -1, 0, -178864, 29166784]$ |
\(y^2=x^3-x^2-178864x+29166784\) |
20286.g3 |
20286x2 |
20286.g |
20286x |
$4$ |
$4$ |
\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 23 \) |
\( 2^{2} \cdot 3^{18} \cdot 7^{8} \cdot 23^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.6.0.1 |
2Cs |
$6.809590022$ |
$1$ |
|
$4$ |
$737280$ |
$2.552677$ |
$154502321244119857/55101928644$ |
$[1, -1, 0, -4929948, -4210664900]$ |
\(y^2+xy=x^3-x^2-4929948x-4210664900\) |
22218.bh3 |
22218bh2 |
22218.bh |
22218bh |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 7 \cdot 23^{2} \) |
\( 2^{2} \cdot 3^{12} \cdot 7^{2} \cdot 23^{8} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.1 |
2Cs |
$3.975705958$ |
$1$ |
|
$4$ |
$1013760$ |
$2.598160$ |
$154502321244119857/55101928644$ |
$[1, 0, 0, -5913702, 5533051680]$ |
\(y^2+xy=x^3-5913702x+5533051680\) |
23184.bt3 |
23184bz2 |
23184.bt |
23184bz |
$4$ |
$4$ |
\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 23 \) |
\( 2^{14} \cdot 3^{18} \cdot 7^{2} \cdot 23^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.6.0.1 |
2Cs |
$12.76816186$ |
$1$ |
|
$3$ |
$368640$ |
$2.272869$ |
$154502321244119857/55101928644$ |
$[0, 0, 0, -1609779, -785893390]$ |
\(y^2=x^3-1609779x-785893390\) |
24150.s3 |
24150j2 |
24150.s |
24150j |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 23 \) |
\( 2^{2} \cdot 3^{12} \cdot 5^{6} \cdot 7^{2} \cdot 23^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.6.0.1 |
2Cs |
$1$ |
$1$ |
|
$2$ |
$245760$ |
$1.835133$ |
$154502321244119857/55101928644$ |
$[1, 1, 0, -279475, -56966375]$ |
\(y^2+xy=x^3+x^2-279475x-56966375\) |
30912.v3 |
30912e2 |
30912.v |
30912e |
$4$ |
$4$ |
\( 2^{6} \cdot 3 \cdot 7 \cdot 23 \) |
\( 2^{20} \cdot 3^{12} \cdot 7^{2} \cdot 23^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.1 |
2Cs |
$1$ |
$4$ |
$2$ |
$3$ |
$368640$ |
$2.070137$ |
$154502321244119857/55101928644$ |
$[0, -1, 0, -715457, -232618815]$ |
\(y^2=x^3-x^2-715457x-232618815\) |
30912.ch3 |
30912ch2 |
30912.ch |
30912ch |
$4$ |
$4$ |
\( 2^{6} \cdot 3 \cdot 7 \cdot 23 \) |
\( 2^{20} \cdot 3^{12} \cdot 7^{2} \cdot 23^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.1 |
2Cs |
$1$ |
$1$ |
|
$3$ |
$368640$ |
$2.070137$ |
$154502321244119857/55101928644$ |
$[0, 1, 0, -715457, 232618815]$ |
\(y^2=x^3+x^2-715457x+232618815\) |
54096.cz3 |
54096cs2 |
54096.cz |
54096cs |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 23 \) |
\( 2^{14} \cdot 3^{12} \cdot 7^{8} \cdot 23^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.1 |
2Cs |
$1$ |
$1$ |
|
$3$ |
$2211840$ |
$2.696518$ |
$154502321244119857/55101928644$ |
$[0, 1, 0, -8764352, -9986678220]$ |
\(y^2=x^3+x^2-8764352x-9986678220\) |
66654.l3 |
66654v2 |
66654.l |
66654v |
$4$ |
$4$ |
\( 2 \cdot 3^{2} \cdot 7 \cdot 23^{2} \) |
\( 2^{2} \cdot 3^{18} \cdot 7^{2} \cdot 23^{8} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.6.0.1 |
2Cs |
$1$ |
$9$ |
$3$ |
$2$ |
$8110080$ |
$3.147469$ |
$154502321244119857/55101928644$ |
$[1, -1, 0, -53223318, -149392395360]$ |
\(y^2+xy=x^3-x^2-53223318x-149392395360\) |
72450.ea3 |
72450eq2 |
72450.ea |
72450eq |
$4$ |
$4$ |
\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 23 \) |
\( 2^{2} \cdot 3^{18} \cdot 5^{6} \cdot 7^{2} \cdot 23^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.6.0.1 |
2Cs |
$4.476943147$ |
$1$ |
|
$4$ |
$1966080$ |
$2.384441$ |
$154502321244119857/55101928644$ |
$[1, -1, 1, -2515280, 1535576847]$ |
\(y^2+xy+y=x^3-x^2-2515280x+1535576847\) |
92736.bg3 |
92736bh2 |
92736.bg |
92736bh |
$4$ |
$4$ |
\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 23 \) |
\( 2^{20} \cdot 3^{18} \cdot 7^{2} \cdot 23^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.6.0.1 |
2Cs |
$1$ |
$1$ |
|
$3$ |
$2949120$ |
$2.619442$ |
$154502321244119857/55101928644$ |
$[0, 0, 0, -6439116, 6287147120]$ |
\(y^2=x^3-6439116x+6287147120\) |
92736.bj3 |
92736fq2 |
92736.bj |
92736fq |
$4$ |
$4$ |
\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 23 \) |
\( 2^{20} \cdot 3^{18} \cdot 7^{2} \cdot 23^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.6.0.1 |
2Cs |
$10.40376757$ |
$1$ |
|
$3$ |
$2949120$ |
$2.619442$ |
$154502321244119857/55101928644$ |
$[0, 0, 0, -6439116, -6287147120]$ |
\(y^2=x^3-6439116x-6287147120\) |
116886.p3 |
116886w2 |
116886.p |
116886w |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 7 \cdot 11^{2} \cdot 23 \) |
\( 2^{2} \cdot 3^{12} \cdot 7^{2} \cdot 11^{6} \cdot 23^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.6.0.1 |
2Cs |
$0.592369540$ |
$1$ |
|
$16$ |
$2457600$ |
$2.229362$ |
$154502321244119857/55101928644$ |
$[1, 0, 1, -1352662, 605225300]$ |
\(y^2+xy+y=x^3-1352662x+605225300\) |
155526.bu3 |
155526bf2 |
155526.bu |
155526bf |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 7^{2} \cdot 23^{2} \) |
\( 2^{2} \cdot 3^{12} \cdot 7^{8} \cdot 23^{8} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.2 |
2Cs |
$1$ |
$4$ |
$2$ |
$2$ |
$48660480$ |
$3.571117$ |
$154502321244119857/55101928644$ |
$[1, 1, 1, -289771399, -1898126497639]$ |
\(y^2+xy+y=x^3+x^2-289771399x-1898126497639\) |
162288.cf3 |
162288v2 |
162288.cf |
162288v |
$4$ |
$4$ |
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 23 \) |
\( 2^{14} \cdot 3^{18} \cdot 7^{8} \cdot 23^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.6.0.1 |
2Cs |
$7.263804512$ |
$1$ |
|
$5$ |
$17694720$ |
$3.245823$ |
$154502321244119857/55101928644$ |
$[0, 0, 0, -78879171, 269561432770]$ |
\(y^2=x^3-78879171x+269561432770\) |
163254.bs3 |
163254ck2 |
163254.bs |
163254ck |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 7 \cdot 13^{2} \cdot 23 \) |
\( 2^{2} \cdot 3^{12} \cdot 7^{2} \cdot 13^{6} \cdot 23^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.6.0.1 |
2Cs |
$1$ |
$1$ |
|
$2$ |
$4423680$ |
$2.312889$ |
$154502321244119857/55101928644$ |
$[1, 0, 1, -1889255, -999351754]$ |
\(y^2+xy+y=x^3-1889255x-999351754\) |
169050.eg3 |
169050gv2 |
169050.eg |
169050gv |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 23 \) |
\( 2^{2} \cdot 3^{12} \cdot 5^{6} \cdot 7^{8} \cdot 23^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.6.0.1 |
2Cs |
$0.875871458$ |
$1$ |
|
$14$ |
$11796480$ |
$2.808090$ |
$154502321244119857/55101928644$ |
$[1, 0, 1, -13694301, 19498383748]$ |
\(y^2+xy+y=x^3-13694301x+19498383748\) |
177744.bj3 |
177744cb2 |
177744.bj |
177744cb |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 7 \cdot 23^{2} \) |
\( 2^{14} \cdot 3^{12} \cdot 7^{2} \cdot 23^{8} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.1 |
2Cs |
$37.90491814$ |
$1$ |
|
$3$ |
$24330240$ |
$3.291309$ |
$154502321244119857/55101928644$ |
$[0, -1, 0, -94619232, -354115307520]$ |
\(y^2=x^3-x^2-94619232x-354115307520\) |
193200.dv3 |
193200bz2 |
193200.dv |
193200bz |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 23 \) |
\( 2^{14} \cdot 3^{12} \cdot 5^{6} \cdot 7^{2} \cdot 23^{2} \) |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.6.0.1 |
2Cs |
$1.267465408$ |
$1$ |
|
$41$ |
$5898240$ |
$2.528282$ |
$154502321244119857/55101928644$ |
$[0, 1, 0, -4471608, 3636904788]$ |
\(y^2=x^3+x^2-4471608x+3636904788\) |
216384.be3 |
216384cu2 |
216384.be |
216384cu |
$4$ |
$4$ |
\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 23 \) |
\( 2^{20} \cdot 3^{12} \cdot 7^{8} \cdot 23^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.1 |
2Cs |
$20.78697468$ |
$1$ |
|
$3$ |
$17694720$ |
$3.043091$ |
$154502321244119857/55101928644$ |
$[0, -1, 0, -35057409, -79858368351]$ |
\(y^2=x^3-x^2-35057409x-79858368351\) |
216384.fj3 |
216384ez2 |
216384.fj |
216384ez |
$4$ |
$4$ |
\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 23 \) |
\( 2^{20} \cdot 3^{12} \cdot 7^{8} \cdot 23^{2} \) |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.1 |
2Cs |
$4.052956367$ |
$1$ |
|
$25$ |
$17694720$ |
$3.043091$ |
$154502321244119857/55101928644$ |
$[0, 1, 0, -35057409, 79858368351]$ |
\(y^2=x^3+x^2-35057409x+79858368351\) |
279174.cc3 |
279174cc2 |
279174.cc |
279174cc |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 7 \cdot 17^{2} \cdot 23 \) |
\( 2^{2} \cdot 3^{12} \cdot 7^{2} \cdot 17^{6} \cdot 23^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.6.0.1 |
2Cs |
$27.85281143$ |
$1$ |
|
$2$ |
$8847360$ |
$2.447021$ |
$154502321244119857/55101928644$ |
$[1, 1, 1, -3230737, -2235775669]$ |
\(y^2+xy+y=x^3+x^2-3230737x-2235775669\) |
348726.b3 |
348726b2 |
348726.b |
348726b |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 7 \cdot 19^{2} \cdot 23 \) |
\( 2^{2} \cdot 3^{12} \cdot 7^{2} \cdot 19^{6} \cdot 23^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.6.0.1 |
2Cs |
$3.725089341$ |
$1$ |
|
$4$ |
$13824000$ |
$2.502632$ |
$154502321244119857/55101928644$ |
$[1, 1, 0, -4035626, 3117787680]$ |
\(y^2+xy=x^3+x^2-4035626x+3117787680\) |
350658.ed3 |
350658ed2 |
350658.ed |
350658ed |
$4$ |
$4$ |
\( 2 \cdot 3^{2} \cdot 7 \cdot 11^{2} \cdot 23 \) |
\( 2^{2} \cdot 3^{18} \cdot 7^{2} \cdot 11^{6} \cdot 23^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.6.0.1 |
2Cs |
$27.35410563$ |
$1$ |
|
$2$ |
$19660800$ |
$2.778667$ |
$154502321244119857/55101928644$ |
$[1, -1, 1, -12173954, -16341083107]$ |
\(y^2+xy+y=x^3-x^2-12173954x-16341083107\) |
466578.cj3 |
466578cj2 |
466578.cj |
466578cj |
$4$ |
$4$ |
\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 23^{2} \) |
\( 2^{2} \cdot 3^{18} \cdot 7^{8} \cdot 23^{8} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.6.0.1 |
2Cs |
$1$ |
$1$ |
|
$2$ |
$389283840$ |
$4.120422$ |
$154502321244119857/55101928644$ |
$[1, -1, 0, -2607942591, 51246807493657]$ |
\(y^2+xy=x^3-x^2-2607942591x+51246807493657\) |
489762.dv3 |
489762dv2 |
489762.dv |
489762dv |
$4$ |
$4$ |
\( 2 \cdot 3^{2} \cdot 7 \cdot 13^{2} \cdot 23 \) |
\( 2^{2} \cdot 3^{18} \cdot 7^{2} \cdot 13^{6} \cdot 23^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.6.0.1 |
2Cs |
$1$ |
$1$ |
|
$2$ |
$35389440$ |
$2.862194$ |
$154502321244119857/55101928644$ |
$[1, -1, 1, -17003291, 26982497351]$ |
\(y^2+xy+y=x^3-x^2-17003291x+26982497351\) |