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 (24 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	Manin constant
5070.j2	5070i2	5070.j	5070i	$2$	$3$	$ 2 \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{3} \cdot 3 \cdot 5^{9} \cdot 13^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.2	3B.1.2	$120$	$16$	$0$	$1$	$1$	$0$	$9072$	$1.010698$	$18573478391/46875000$	$1.02244$	$4.11636$	$[1, 0, 1, 1686, 49012]$	$y^2+xy+y=x^3+1686x+49012$	3.8.0-3.a.1.1, 120.16.0.?	$[ ]$	$1$
5070.v2	5070u2	5070.v	5070u	$2$	$3$	$ 2 \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{3} \cdot 3 \cdot 5^{9} \cdot 13^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$1$	$1$	$0$	$117936$	$2.293171$	$18573478391/46875000$	$1.02244$	$5.92031$	$[1, 0, 0, 285015, 107394897]$	$y^2+xy=x^3+285015x+107394897$	3.4.0.a.1, 39.8.0-3.a.1.2, 120.8.0.?, 1560.16.0.?	$[ ]$	$1$
15210.e2	15210j2	15210.e	15210j	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{3} \cdot 3^{7} \cdot 5^{9} \cdot 13^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$1$	$1$	$0$	$943488$	$2.842480$	$18573478391/46875000$	$1.02244$	$5.92940$	$[1, -1, 0, 2565135, -2899662219]$	$y^2+xy=x^3-x^2+2565135x-2899662219$	3.4.0.a.1, 39.8.0-3.a.1.1, 120.8.0.?, 1560.16.0.?	$[ ]$	$1$
15210.br2	15210bp2	15210.br	15210bp	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{3} \cdot 3^{7} \cdot 5^{9} \cdot 13^{4} $	$0$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.1	3B.1.1	$120$	$16$	$0$	$1$	$1$	$2$	$72576$	$1.560003$	$18573478391/46875000$	$1.02244$	$4.33126$	$[1, -1, 1, 15178, -1323331]$	$y^2+xy+y=x^3-x^2+15178x-1323331$	3.8.0-3.a.1.2, 120.16.0.?	$[ ]$	$1$
25350.s2	25350d2	25350.s	25350d	$2$	$3$	$ 2 \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ - 2^{3} \cdot 3 \cdot 5^{15} \cdot 13^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$11.59528861$	$1$	$0$	$2830464$	$3.097893$	$18573478391/46875000$	$1.02244$	$5.93296$	$[1, 1, 0, 7125375, 13424362125]$	$y^2+xy=x^3+x^2+7125375x+13424362125$	3.4.0.a.1, 120.8.0.?, 195.8.0.?, 312.8.0.?, 1560.16.0.?	$[(20191505/8, 90653124605/8)]$	$1$
25350.cb2	25350bz2	25350.cb	25350bz	$2$	$3$	$ 2 \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ - 2^{3} \cdot 3 \cdot 5^{15} \cdot 13^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$120$	$16$	$0$	$1$	$1$	$0$	$217728$	$1.815416$	$18573478391/46875000$	$1.02244$	$4.41532$	$[1, 1, 1, 42162, 6126531]$	$y^2+xy+y=x^3+x^2+42162x+6126531$	3.4.0.a.1, 15.8.0-3.a.1.1, 24.8.0-3.a.1.6, 120.16.0.?	$[ ]$	$1$
40560.f2	40560bj2	40560.f	40560bj	$2$	$3$	$ 2^{4} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{15} \cdot 3 \cdot 5^{9} \cdot 13^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$120$	$16$	$0$	$1$	$1$	$0$	$217728$	$1.703846$	$18573478391/46875000$	$1.02244$	$4.09356$	$[0, -1, 0, 26984, -3136784]$	$y^2=x^3-x^2+26984x-3136784$	3.4.0.a.1, 12.8.0-3.a.1.2, 120.16.0.?	$[ ]$	$1$
40560.bb2	40560bs2	40560.bb	40560bs	$2$	$3$	$ 2^{4} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{15} \cdot 3 \cdot 5^{9} \cdot 13^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$2.681849876$	$1$	$2$	$2830464$	$2.986320$	$18573478391/46875000$	$1.02244$	$5.54397$	$[0, -1, 0, 4560240, -6873273408]$	$y^2=x^3-x^2+4560240x-6873273408$	3.4.0.a.1, 120.8.0.?, 156.8.0.?, 1560.16.0.?	$[(1864, 90000)]$	$1$
76050.z2	76050bn2	76050.z	76050bn	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 13^{2} $	$ - 2^{3} \cdot 3^{7} \cdot 5^{15} \cdot 13^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$120$	$16$	$0$	$1$	$1$	$0$	$1741824$	$2.364723$	$18573478391/46875000$	$1.02244$	$4.57022$	$[1, -1, 0, 379458, -165036884]$	$y^2+xy=x^3-x^2+379458x-165036884$	3.4.0.a.1, 15.8.0-3.a.1.2, 24.8.0-3.a.1.5, 120.16.0.?	$[ ]$	$1$
76050.fk2	76050el2	76050.fk	76050el	$2$	$3$	$ 2 \cdot 3^{2} \cdot 5^{2} \cdot 13^{2} $	$ - 2^{3} \cdot 3^{7} \cdot 5^{15} \cdot 13^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$14.58964418$	$1$	$0$	$22643712$	$3.647198$	$18573478391/46875000$	$1.02244$	$5.93951$	$[1, -1, 1, 64128370, -362393649003]$	$y^2+xy+y=x^3-x^2+64128370x-362393649003$	3.4.0.a.1, 120.8.0.?, 195.8.0.?, 312.8.0.?, 1560.16.0.?	$[(64087439/29, 514733951115/29)]$	$1$
121680.cc2	121680do2	121680.cc	121680do	$2$	$3$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{15} \cdot 3^{7} \cdot 5^{9} \cdot 13^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$20.35675951$	$1$	$0$	$22643712$	$3.535625$	$18573478391/46875000$	$1.02244$	$5.58676$	$[0, 0, 0, 41042157, 185537339858]$	$y^2=x^3+41042157x+185537339858$	3.4.0.a.1, 120.8.0.?, 156.8.0.?, 1560.16.0.?	$[(-647924663/554, 50863463196525/554)]$	$1$
121680.dr2	121680ey2	121680.dr	121680ey	$2$	$3$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{15} \cdot 3^{7} \cdot 5^{9} \cdot 13^{4} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$120$	$16$	$0$	$0.158902240$	$1$	$32$	$1741824$	$2.253151$	$18573478391/46875000$	$1.02244$	$4.27243$	$[0, 0, 0, 242853, 84450314]$	$y^2=x^3+242853x+84450314$	3.4.0.a.1, 12.8.0-3.a.1.1, 120.16.0.?	$[(493, 18000), (13, 9360)]$	$1$
162240.j2	162240hs2	162240.j	162240hs	$2$	$3$	$ 2^{6} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{21} \cdot 3 \cdot 5^{9} \cdot 13^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$18.10043832$	$1$	$0$	$22643712$	$3.332893$	$18573478391/46875000$	$1.02244$	$5.25000$	$[0, -1, 0, 18240959, 54967946305]$	$y^2=x^3-x^2+18240959x+54967946305$	3.4.0.a.1, 120.8.0.?, 312.8.0.?, 390.8.0.?, 1560.16.0.?	$[(33029001/395, 14949383429824/395)]$	$1$
162240.ds2	162240hh2	162240.ds	162240hh	$2$	$3$	$ 2^{6} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{21} \cdot 3 \cdot 5^{9} \cdot 13^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$120$	$16$	$0$	$1$	$1$	$0$	$1741824$	$2.050419$	$18573478391/46875000$	$1.02244$	$3.96719$	$[0, -1, 0, 107935, 24986337]$	$y^2=x^3-x^2+107935x+24986337$	3.4.0.a.1, 24.8.0-3.a.1.1, 30.8.0-3.a.1.1, 120.16.0.?	$[ ]$	$1$
162240.fw2	162240bt2	162240.fw	162240bt	$2$	$3$	$ 2^{6} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{21} \cdot 3 \cdot 5^{9} \cdot 13^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$59.13891715$	$1$	$0$	$22643712$	$3.332893$	$18573478391/46875000$	$1.02244$	$5.25000$	$[0, 1, 0, 18240959, -54967946305]$	$y^2=x^3+x^2+18240959x-54967946305$	3.4.0.a.1, 120.8.0.?, 312.8.0.?, 780.8.0.?, 1560.16.0.?	$[(564855261634588468972181479/179635098595, 13751932585345725193172013330802370822208/179635098595)]$	$1$
162240.gs2	162240e2	162240.gs	162240e	$2$	$3$	$ 2^{6} \cdot 3 \cdot 5 \cdot 13^{2} $	$ - 2^{21} \cdot 3 \cdot 5^{9} \cdot 13^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$120$	$16$	$0$	$1$	$1$	$0$	$1741824$	$2.050419$	$18573478391/46875000$	$1.02244$	$3.96719$	$[0, 1, 0, 107935, -24986337]$	$y^2=x^3+x^2+107935x-24986337$	3.4.0.a.1, 24.8.0-3.a.1.3, 60.8.0-3.a.1.4, 120.16.0.?	$[ ]$	$1$
202800.gn2	202800bt2	202800.gn	202800bt	$2$	$3$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ - 2^{15} \cdot 3 \cdot 5^{15} \cdot 13^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$32.61843782$	$1$	$0$	$67931136$	$3.791039$	$18573478391/46875000$	$1.02244$	$5.60403$	$[0, 1, 0, 114005992, -858931164012]$	$y^2=x^3+x^2+114005992x-858931164012$	3.4.0.a.1, 120.8.0.?, 312.8.0.?, 780.8.0.?, 1560.16.0.?	$[(20923107349448937/953528, 3238265017030572293296875/953528)]$	$1$
202800.ji2	202800cs2	202800.ji	202800cs	$2$	$3$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 13^{2} $	$ - 2^{15} \cdot 3 \cdot 5^{15} \cdot 13^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$120$	$16$	$0$	$14.13014676$	$1$	$0$	$5225472$	$2.508564$	$18573478391/46875000$	$1.02244$	$4.34464$	$[0, 1, 0, 674592, -390748812]$	$y^2=x^3+x^2+674592x-390748812$	3.4.0.a.1, 24.8.0-3.a.1.8, 60.8.0-3.a.1.1, 120.16.0.?	$[(4212778/87, 8262796976/87)]$	$1$
248430.br2	248430br2	248430.br	248430br	$2$	$3$	$ 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13^{2} $	$ - 2^{3} \cdot 3 \cdot 5^{9} \cdot 7^{6} \cdot 13^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$840$	$16$	$0$	$1.137594297$	$1$	$4$	$3265920$	$1.983652$	$18573478391/46875000$	$1.02244$	$3.76663$	$[1, 1, 0, 82638, -16728564]$	$y^2+xy=x^3+x^2+82638x-16728564$	3.4.0.a.1, 21.8.0-3.a.1.2, 120.8.0.?, 840.16.0.?	$[(587, 15019)]$	$1$
248430.gi2	248430gi2	248430.gi	248430gi	$2$	$3$	$ 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13^{2} $	$ - 2^{3} \cdot 3 \cdot 5^{9} \cdot 7^{6} \cdot 13^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$10920$	$16$	$0$	$37.08700701$	$1$	$0$	$42456960$	$3.266129$	$18573478391/46875000$	$1.02244$	$5.00544$	$[1, 1, 1, 13965734, -36822483937]$	$y^2+xy+y=x^3+x^2+13965734x-36822483937$	3.4.0.a.1, 120.8.0.?, 273.8.0.?, 10920.16.0.?	$[(89705190644542339/4386199, 30193096154742664943074597/4386199)]$	$1$
486720.co2	486720co2	486720.co	486720co	$2$	$3$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{21} \cdot 3^{7} \cdot 5^{9} \cdot 13^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$120$	$16$	$0$	$6.733031281$	$1$	$0$	$13934592$	$2.599724$	$18573478391/46875000$	$1.02244$	$4.13773$	$[0, 0, 0, 971412, 675602512]$	$y^2=x^3+971412x+675602512$	3.4.0.a.1, 24.8.0-3.a.1.4, 60.8.0-3.a.1.3, 120.16.0.?	$[(-12886/5, 770112/5)]$	$1$
486720.fx2	486720fx2	486720.fx	486720fx	$2$	$3$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{21} \cdot 3^{7} \cdot 5^{9} \cdot 13^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$120$	$16$	$0$	$1$	$1$	$0$	$13934592$	$2.599724$	$18573478391/46875000$	$1.02244$	$4.13773$	$[0, 0, 0, 971412, -675602512]$	$y^2=x^3+971412x-675602512$	3.4.0.a.1, 24.8.0-3.a.1.2, 30.8.0-3.a.1.2, 120.16.0.?	$[ ]$	$1$
486720.kx2	486720kx2	486720.kx	486720kx	$2$	$3$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{21} \cdot 3^{7} \cdot 5^{9} \cdot 13^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$4.153721374$	$1$	$2$	$181149696$	$3.882198$	$18573478391/46875000$	$1.02244$	$5.31292$	$[0, 0, 0, 164168628, -1484298718864]$	$y^2=x^3+164168628x-1484298718864$	3.4.0.a.1, 120.8.0.?, 312.8.0.?, 390.8.0.?, 1560.16.0.?	$[(7432, 382500)]$	$1$
486720.om2	486720om2	486720.om	486720om	$2$	$3$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 13^{2} $	$ - 2^{21} \cdot 3^{7} \cdot 5^{9} \cdot 13^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$1560$	$16$	$0$	$1$	$1$	$0$	$181149696$	$3.882198$	$18573478391/46875000$	$1.02244$	$5.31292$	$[0, 0, 0, 164168628, 1484298718864]$	$y^2=x^3+164168628x+1484298718864$	3.4.0.a.1, 120.8.0.?, 312.8.0.?, 780.8.0.?, 1560.16.0.?	$[ ]$	$1$

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Elliptic curves over $\Q$
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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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