LMFDB - Elliptic curve search results

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Conductor	Discriminant	j-invariant	Rank

Bad$\ p$	Curves per isogeny class	Complex multiplication	Torsion

Isogeny class degree	Cyclic isogeny degree	Isogeny class size	Integral points

Analytic order of Ш	$p\ $div$\ $\|Ш\|	Regulator	Reduction	Faltings height

Galois image	Adelic level	Adelic index	Adelic genus

Nonmax$\ \ell$	$abc$ quality	Szpiro ratio	Manin constant

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Results (28 matches)

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	Sato-Tate	Nonmax $\ell$	$\ell$-adic images	mod-$\ell$ images	Adelic level	Adelic index	Adelic genus	Regulator	$Ш_{\textrm{an}}$	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
6050.e2	6050r1	6050.e	6050r	$2$	$3$	$ 2 \cdot 5^{2} \cdot 11^{2} $	$ 2^{3} \cdot 5^{8} \cdot 11^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.2.0.2, 3.4.0.1	3B	$264$	$16$	$0$	$0.473130687$	$1$	$4$	$2880$	$0.342610$	$18865/8$	$0.81990$	$3.15996$	$[1, 0, 1, -201, 548]$	$y^2+xy+y=x^3-201x+548$	3.4.0.a.1, 8.2.0.b.1, 24.8.0.b.1, 33.8.0-3.a.1.2, 264.16.0.?	$[(2, 11)]$
6050.r2	6050i1	6050.r	6050i	$2$	$3$	$ 2 \cdot 5^{2} \cdot 11^{2} $	$ 2^{3} \cdot 5^{2} \cdot 11^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.2.0.2, 3.4.0.1	3B	$120$	$16$	$0$	$1$	$1$	$0$	$6336$	$0.736839$	$18865/8$	$0.81990$	$3.70324$	$[1, 1, 0, -970, -6420]$	$y^2+xy=x^3+x^2-970x-6420$	3.4.0.a.1, 8.2.0.b.1, 15.8.0-3.a.1.2, 24.8.0.b.1, 120.16.0.?	$[ ]$
6050.w2	6050bm1	6050.w	6050bm	$2$	$3$	$ 2 \cdot 5^{2} \cdot 11^{2} $	$ 2^{3} \cdot 5^{8} \cdot 11^{8} $	$0$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.2.0.2, 3.8.0.1	3B.1.1	$24$	$16$	$0$	$1$	$1$	$2$	$31680$	$1.541557$	$18865/8$	$0.81990$	$4.81220$	$[1, 0, 0, -24263, -753983]$	$y^2+xy=x^3-24263x-753983$	3.8.0-3.a.1.2, 8.2.0.b.1, 24.16.0-24.b.1.8	$[ ]$
6050.bm2	6050bd1	6050.bm	6050bd	$2$	$3$	$ 2 \cdot 5^{2} \cdot 11^{2} $	$ 2^{3} \cdot 5^{2} \cdot 11^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.2.0.2, 3.4.0.1	3B	$1320$	$16$	$0$	$0.731862979$	$1$	$2$	$576$	$-0.462109$	$18865/8$	$0.81990$	$2.05100$	$[1, 1, 1, -8, 1]$	$y^2+xy+y=x^3+x^2-8x+1$	3.4.0.a.1, 8.2.0.b.1, 24.8.0.b.1, 165.8.0.?, 1320.16.0.?	$[(-1, 3)]$
48400.n2	48400cl1	48400.n	48400cl	$2$	$3$	$ 2^{4} \cdot 5^{2} \cdot 11^{2} $	$ 2^{15} \cdot 5^{2} \cdot 11^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.2.0.2, 3.4.0.1	3B	$120$	$16$	$0$	$4.129190955$	$1$	$2$	$152064$	$1.429987$	$18865/8$	$0.81990$	$3.76044$	$[0, 1, 0, -15528, 379828]$	$y^2=x^3+x^2-15528x+379828$	3.4.0.a.1, 8.2.0.b.1, 24.8.0.b.1, 60.8.0-3.a.1.2, 120.16.0.?	$[(12, 442)]$
48400.s2	48400ck1	48400.s	48400ck	$2$	$3$	$ 2^{4} \cdot 5^{2} \cdot 11^{2} $	$ 2^{15} \cdot 5^{2} \cdot 11^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.2.0.2, 3.4.0.1	3B	$1320$	$16$	$0$	$0.550665800$	$1$	$6$	$13824$	$0.231039$	$18865/8$	$0.81990$	$2.42671$	$[0, 1, 0, -128, -332]$	$y^2=x^3+x^2-128x-332$	3.4.0.a.1, 8.2.0.b.1, 24.8.0.b.1, 660.8.0.?, 1320.16.0.?	$[(-6, 16)]$
48400.cz2	48400dc1	48400.cz	48400dc	$2$	$3$	$ 2^{4} \cdot 5^{2} \cdot 11^{2} $	$ 2^{15} \cdot 5^{8} \cdot 11^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.2.0.2, 3.4.0.1	3B	$264$	$16$	$0$	$1$	$1$	$0$	$69120$	$1.035757$	$18865/8$	$0.81990$	$3.32189$	$[0, -1, 0, -3208, -35088]$	$y^2=x^3-x^2-3208x-35088$	3.4.0.a.1, 8.2.0.b.1, 24.8.0.b.1, 132.8.0.?, 264.16.0.?	$[ ]$
48400.df2	48400db1	48400.df	48400db	$2$	$3$	$ 2^{4} \cdot 5^{2} \cdot 11^{2} $	$ 2^{15} \cdot 5^{8} \cdot 11^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.2.0.2, 3.4.0.1	3B	$24$	$16$	$0$	$1$	$1$	$0$	$760320$	$2.234707$	$18865/8$	$0.81990$	$4.65563$	$[0, -1, 0, -388208, 48254912]$	$y^2=x^3-x^2-388208x+48254912$	3.4.0.a.1, 8.2.0.b.1, 12.8.0-3.a.1.1, 24.16.0-24.b.1.2	$[ ]$
54450.bi2	54450bw1	54450.bi	54450bw	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 11^{2} $	$ 2^{3} \cdot 3^{6} \cdot 5^{2} \cdot 11^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.2.0.2, 3.4.0.1	3B	$1320$	$16$	$0$	$1.173302542$	$1$	$4$	$13824$	$0.087198$	$18865/8$	$0.81990$	$2.24221$	$[1, -1, 0, -72, -104]$	$y^2+xy=x^3-x^2-72x-104$	3.4.0.a.1, 8.2.0.b.1, 24.8.0.b.1, 165.8.0.?, 1320.16.0.?	$[(-7, 8)]$
54450.bj2	54450db1	54450.bj	54450db	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 11^{2} $	$ 2^{3} \cdot 3^{6} \cdot 5^{8} \cdot 11^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.2.0.2, 3.8.0.2	3B.1.2	$24$	$16$	$0$	$1$	$1$	$0$	$760320$	$2.090866$	$18865/8$	$0.81990$	$4.44706$	$[1, -1, 0, -218367, 20357541]$	$y^2+xy=x^3-x^2-218367x+20357541$	3.8.0-3.a.1.1, 8.2.0.b.1, 24.16.0-24.b.1.4	$[ ]$
54450.fz2	54450gu1	54450.fz	54450gu	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 11^{2} $	$ 2^{3} \cdot 3^{6} \cdot 5^{8} \cdot 11^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.2.0.2, 3.4.0.1	3B	$264$	$16$	$0$	$2.260867966$	$1$	$2$	$69120$	$0.891916$	$18865/8$	$0.81990$	$3.12773$	$[1, -1, 1, -1805, -14803]$	$y^2+xy+y=x^3-x^2-1805x-14803$	3.4.0.a.1, 8.2.0.b.1, 24.8.0.b.1, 33.8.0-3.a.1.1, 264.16.0.?	$[(-27, 130)]$
54450.ga2	54450fh1	54450.ga	54450fh	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 11^{2} $	$ 2^{3} \cdot 3^{6} \cdot 5^{2} \cdot 11^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.2.0.2, 3.4.0.1	3B	$120$	$16$	$0$	$1$	$1$	$0$	$152064$	$1.286146$	$18865/8$	$0.81990$	$3.56154$	$[1, -1, 1, -8735, 164607]$	$y^2+xy+y=x^3-x^2-8735x+164607$	3.4.0.a.1, 8.2.0.b.1, 15.8.0-3.a.1.1, 24.8.0.b.1, 120.16.0.?	$[ ]$
193600.bh2	193600m1	193600.bh	193600m	$2$	$3$	$ 2^{6} \cdot 5^{2} \cdot 11^{2} $	$ 2^{21} \cdot 5^{8} \cdot 11^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.2.0.2, 3.4.0.1	3B	$264$	$16$	$0$	$1$	$1$	$0$	$552960$	$1.382332$	$18865/8$	$0.81990$	$3.28524$	$[0, 1, 0, -12833, -293537]$	$y^2=x^3+x^2-12833x-293537$	3.4.0.a.1, 8.2.0.b.1, 24.8.0.b.1, 132.8.0.?, 264.16.0.?	$[ ]$
193600.bi2	193600gh1	193600.bi	193600gh	$2$	$3$	$ 2^{6} \cdot 5^{2} \cdot 11^{2} $	$ 2^{21} \cdot 5^{2} \cdot 11^{2} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.2.0.2, 3.4.0.1	3B	$1320$	$16$	$0$	$1.997587451$	$1$	$12$	$110592$	$0.577612$	$18865/8$	$0.81990$	$2.49199$	$[0, 1, 0, -513, 2143]$	$y^2=x^3+x^2-513x+2143$	3.4.0.a.1, 8.2.0.b.1, 24.8.0.b.1, 330.8.0.?, 1320.16.0.?	$[(-21, 64), (107, 1088)]$
193600.bv2	193600gk1	193600.bv	193600gk	$2$	$3$	$ 2^{6} \cdot 5^{2} \cdot 11^{2} $	$ 2^{21} \cdot 5^{2} \cdot 11^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.2.0.2, 3.4.0.1	3B	$120$	$16$	$0$	$1$	$1$	$0$	$1216512$	$1.776560$	$18865/8$	$0.81990$	$3.67385$	$[0, 1, 0, -62113, -3100737]$	$y^2=x^3+x^2-62113x-3100737$	3.4.0.a.1, 8.2.0.b.1, 24.8.0.b.1, 30.8.0-3.a.1.1, 120.16.0.?	$[ ]$
193600.bw2	193600p1	193600.bw	193600p	$2$	$3$	$ 2^{6} \cdot 5^{2} \cdot 11^{2} $	$ 2^{21} \cdot 5^{8} \cdot 11^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.2.0.2, 3.4.0.1	3B	$24$	$16$	$0$	$1$	$1$	$0$	$6082560$	$2.581280$	$18865/8$	$0.81990$	$4.46709$	$[0, 1, 0, -1552833, 384486463]$	$y^2=x^3+x^2-1552833x+384486463$	3.4.0.a.1, 8.2.0.b.1, 12.8.0-3.a.1.3, 24.16.0-24.b.1.3	$[ ]$
193600.hu2	193600ep1	193600.hu	193600ep	$2$	$3$	$ 2^{6} \cdot 5^{2} \cdot 11^{2} $	$ 2^{21} \cdot 5^{2} \cdot 11^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.2.0.2, 3.4.0.1	3B	$120$	$16$	$0$	$4.777934066$	$1$	$0$	$1216512$	$1.776560$	$18865/8$	$0.81990$	$3.67385$	$[0, -1, 0, -62113, 3100737]$	$y^2=x^3-x^2-62113x+3100737$	3.4.0.a.1, 8.2.0.b.1, 24.8.0.b.1, 60.8.0-3.a.1.4, 120.16.0.?	$[(1299/5, 13068/5)]$
193600.hv2	193600iw1	193600.hv	193600iw	$2$	$3$	$ 2^{6} \cdot 5^{2} \cdot 11^{2} $	$ 2^{21} \cdot 5^{8} \cdot 11^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.2.0.2, 3.4.0.1	3B	$24$	$16$	$0$	$17.59480432$	$1$	$0$	$6082560$	$2.581280$	$18865/8$	$0.81990$	$4.46709$	$[0, -1, 0, -1552833, -384486463]$	$y^2=x^3-x^2-1552833x-384486463$	3.4.0.a.1, 6.8.0-3.a.1.1, 8.2.0.b.1, 24.16.0-24.b.1.5	$[(544788361/261, 12554786950208/261)]$
193600.ii2	193600iy1	193600.ii	193600iy	$2$	$3$	$ 2^{6} \cdot 5^{2} \cdot 11^{2} $	$ 2^{21} \cdot 5^{8} \cdot 11^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.2.0.2, 3.4.0.1	3B	$264$	$16$	$0$	$10.54956404$	$1$	$0$	$552960$	$1.382332$	$18865/8$	$0.81990$	$3.28524$	$[0, -1, 0, -12833, 293537]$	$y^2=x^3-x^2-12833x+293537$	3.4.0.a.1, 8.2.0.b.1, 24.8.0.b.1, 66.8.0-3.a.1.1, 264.16.0.?	$[(8608/19, 157131/19)]$
193600.ij2	193600eu1	193600.ij	193600eu	$2$	$3$	$ 2^{6} \cdot 5^{2} \cdot 11^{2} $	$ 2^{21} \cdot 5^{2} \cdot 11^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.2.0.2, 3.4.0.1	3B	$1320$	$16$	$0$	$2.795504930$	$1$	$0$	$110592$	$0.577612$	$18865/8$	$0.81990$	$2.49199$	$[0, -1, 0, -513, -2143]$	$y^2=x^3-x^2-513x-2143$	3.4.0.a.1, 8.2.0.b.1, 24.8.0.b.1, 660.8.0.?, 1320.16.0.?	$[(-131/3, 1216/3)]$
296450.n2	296450n1	296450.n	296450n	$2$	$3$	$ 2 \cdot 5^{2} \cdot 7^{2} \cdot 11^{2} $	$ 2^{3} \cdot 5^{2} \cdot 7^{6} \cdot 11^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.2.0.2, 3.4.0.1	3B	$840$	$16$	$0$	$2.648463471$	$1$	$2$	$2395008$	$1.709795$	$18865/8$	$0.81990$	$3.48602$	$[1, 0, 1, -47556, 2059418]$	$y^2+xy+y=x^3-47556x+2059418$	3.4.0.a.1, 8.2.0.b.1, 24.8.0.b.1, 105.8.0.?, 840.16.0.?	$[(-232, 902)]$
296450.ek2	296450ek1	296450.ek	296450ek	$2$	$3$	$ 2 \cdot 5^{2} \cdot 7^{2} \cdot 11^{2} $	$ 2^{3} \cdot 5^{8} \cdot 7^{6} \cdot 11^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.2.0.2, 3.4.0.1	3B	$1848$	$16$	$0$	$1$	$1$	$0$	$1088640$	$1.315565$	$18865/8$	$0.81990$	$3.11055$	$[1, 1, 0, -9825, -197875]$	$y^2+xy=x^3+x^2-9825x-197875$	3.4.0.a.1, 8.2.0.b.1, 24.8.0.b.1, 231.8.0.?, 1848.16.0.?	$[ ]$
296450.gr2	296450gr1	296450.gr	296450gr	$2$	$3$	$ 2 \cdot 5^{2} \cdot 7^{2} \cdot 11^{2} $	$ 2^{3} \cdot 5^{2} \cdot 7^{6} \cdot 11^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.2.0.2, 3.4.0.1	3B	$9240$	$16$	$0$	$1$	$1$	$0$	$217728$	$0.510846$	$18865/8$	$0.81990$	$2.34413$	$[1, 0, 0, -393, -1583]$	$y^2+xy=x^3-393x-1583$	3.4.0.a.1, 8.2.0.b.1, 24.8.0.b.1, 1155.8.0.?, 9240.16.0.?	$[ ]$
296450.kj2	296450kj1	296450.kj	296450kj	$2$	$3$	$ 2 \cdot 5^{2} \cdot 7^{2} \cdot 11^{2} $	$ 2^{3} \cdot 5^{8} \cdot 7^{6} \cdot 11^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.2.0.2, 3.4.0.1	3B	$168$	$16$	$0$	$13.48129185$	$1$	$0$	$11975040$	$2.514515$	$18865/8$	$0.81990$	$4.25244$	$[1, 1, 1, -1188888, 257427281]$	$y^2+xy+y=x^3+x^2-1188888x+257427281$	3.4.0.a.1, 8.2.0.b.1, 21.8.0-3.a.1.1, 24.8.0.b.1, 168.16.0.?	$[(3443679/161, 41837161997/161)]$
435600.ii2	435600ii1	435600.ii	435600ii	$2$	$3$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 11^{2} $	$ 2^{15} \cdot 3^{6} \cdot 5^{2} \cdot 11^{8} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.2.0.2, 3.4.0.1	3B	$120$	$16$	$0$	$2.712497321$	$1$	$8$	$3649536$	$1.979292$	$18865/8$	$0.81990$	$3.63176$	$[0, 0, 0, -139755, -10395110]$	$y^2=x^3-139755x-10395110$	3.4.0.a.1, 8.2.0.b.1, 24.8.0.b.1, 60.8.0-3.a.1.1, 120.16.0.?	$[(-121, 2178), (-1331/3, 71632/3)]$
435600.ij2	435600ij1	435600.ij	435600ij	$2$	$3$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 11^{2} $	$ 2^{15} \cdot 3^{6} \cdot 5^{8} \cdot 11^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.2.0.2, 3.4.0.1	3B	$264$	$16$	$0$	$2.428213379$	$1$	$2$	$1658880$	$1.585064$	$18865/8$	$0.81990$	$3.26742$	$[0, 0, 0, -28875, 976250]$	$y^2=x^3-28875x+976250$	3.4.0.a.1, 8.2.0.b.1, 24.8.0.b.1, 132.8.0.?, 264.16.0.?	$[(181, 1296)]$
435600.me2	435600me1	435600.me	435600me	$2$	$3$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 11^{2} $	$ 2^{15} \cdot 3^{6} \cdot 5^{8} \cdot 11^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.2.0.2, 3.4.0.1	3B	$24$	$16$	$0$	$5.968936744$	$1$	$0$	$18247680$	$2.784012$	$18865/8$	$0.81990$	$4.37547$	$[0, 0, 0, -3493875, -1299388750]$	$y^2=x^3-3493875x-1299388750$	3.4.0.a.1, 8.2.0.b.1, 12.8.0-3.a.1.2, 24.16.0-24.b.1.6	$[(-8591/4, 1314423/4)]$
435600.mf2	435600mf1	435600.mf	435600mf	$2$	$3$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 11^{2} $	$ 2^{15} \cdot 3^{6} \cdot 5^{2} \cdot 11^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.2.0.2, 3.4.0.1	3B	$1320$	$16$	$0$	$1$	$1$	$0$	$331776$	$0.780345$	$18865/8$	$0.81990$	$2.52372$	$[0, 0, 0, -1155, 7810]$	$y^2=x^3-1155x+7810$	3.4.0.a.1, 8.2.0.b.1, 24.8.0.b.1, 660.8.0.?, 1320.16.0.?	$[ ]$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

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Results (28 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Refine search