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 (36 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	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
1664.a1	1664n1	1664.a	1664n	$1$	$1$	$ 2^{7} \cdot 13 $	$ - 2^{13} \cdot 13 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$0.178682343$	$1$		$22$	$320$	$-0.353944$	$-864/13$	$0.75650$	$2.57090$	$[0, 0, 0, -4, 16]$	$y^2=x^3-4x+16$	104.2.0.?	$[(2, 4), (-2, 4)]$
1664.b1	1664t1	1664.b	1664t	$1$	$1$	$ 2^{7} \cdot 13 $	$ - 2^{7} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1.065988139$	$1$		$2$	$160$	$-0.700518$	$-864/13$	$0.75650$	$2.01018$	$[0, 0, 0, -1, -2]$	$y^2=x^3-x-2$	104.2.0.?	$[(2, 2)]$
1664.s1	1664m1	1664.s	1664m	$1$	$1$	$ 2^{7} \cdot 13 $	$ - 2^{13} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1$	$1$		$0$	$320$	$-0.353944$	$-864/13$	$0.75650$	$2.57090$	$[0, 0, 0, -4, -16]$	$y^2=x^3-4x-16$	104.2.0.?	$[ ]$
1664.t1	1664i1	1664.t	1664i	$1$	$1$	$ 2^{7} \cdot 13 $	$ - 2^{7} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1$	$1$		$0$	$160$	$-0.700518$	$-864/13$	$0.75650$	$2.01018$	$[0, 0, 0, -1, 2]$	$y^2=x^3-x+2$	104.2.0.?	$[ ]$
14976.a1	14976bj1	14976.a	14976bj	$1$	$1$	$ 2^{7} \cdot 3^{2} \cdot 13 $	$ - 2^{7} \cdot 3^{6} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1$	$1$		$0$	$2240$	$-0.151211$	$-864/13$	$0.75650$	$2.23639$	$[0, 0, 0, -9, -54]$	$y^2=x^3-9x-54$	104.2.0.?	$[ ]$
14976.b1	14976u1	14976.b	14976u	$1$	$1$	$ 2^{7} \cdot 3^{2} \cdot 13 $	$ - 2^{7} \cdot 3^{6} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1.870132886$	$1$		$2$	$2240$	$-0.151211$	$-864/13$	$0.75650$	$2.23639$	$[0, 0, 0, -9, 54]$	$y^2=x^3-9x+54$	104.2.0.?	$[(-2, 8)]$
14976.bi1	14976m1	14976.bi	14976m	$1$	$1$	$ 2^{7} \cdot 3^{2} \cdot 13 $	$ - 2^{13} \cdot 3^{6} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1$	$1$		$0$	$4480$	$0.195363$	$-864/13$	$0.75650$	$2.66897$	$[0, 0, 0, -36, -432]$	$y^2=x^3-36x-432$	104.2.0.?	$[ ]$
14976.bj1	14976l1	14976.bj	14976l	$1$	$1$	$ 2^{7} \cdot 3^{2} \cdot 13 $	$ - 2^{13} \cdot 3^{6} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1$	$1$		$0$	$4480$	$0.195363$	$-864/13$	$0.75650$	$2.66897$	$[0, 0, 0, -36, 432]$	$y^2=x^3-36x+432$	104.2.0.?	$[ ]$
21632.a1	21632v1	21632.a	21632v	$1$	$1$	$ 2^{7} \cdot 13^{2} $	$ - 2^{7} \cdot 13^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1.926515910$	$1$		$2$	$26880$	$0.581958$	$-864/13$	$0.75650$	$3.03540$	$[0, 0, 0, -169, -4394]$	$y^2=x^3-169x-4394$	104.2.0.?	$[(78, 676)]$
21632.b1	21632u1	21632.b	21632u	$1$	$1$	$ 2^{7} \cdot 13^{2} $	$ - 2^{13} \cdot 13^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$0.341342227$	$1$		$4$	$53760$	$0.928531$	$-864/13$	$0.75650$	$3.45204$	$[0, 0, 0, -676, 35152]$	$y^2=x^3-676x+35152$	104.2.0.?	$[(78, 676)]$
21632.bm1	21632bn1	21632.bm	21632bn	$1$	$1$	$ 2^{7} \cdot 13^{2} $	$ - 2^{7} \cdot 13^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1$	$1$		$0$	$26880$	$0.581958$	$-864/13$	$0.75650$	$3.03540$	$[0, 0, 0, -169, 4394]$	$y^2=x^3-169x+4394$	104.2.0.?	$[ ]$
21632.bn1	21632t1	21632.bn	21632t	$1$	$1$	$ 2^{7} \cdot 13^{2} $	$ - 2^{13} \cdot 13^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$3.184709553$	$1$		$0$	$53760$	$0.928531$	$-864/13$	$0.75650$	$3.45204$	$[0, 0, 0, -676, -35152]$	$y^2=x^3-676x-35152$	104.2.0.?	$[(988/3, 29744/3)]$
41600.a1	41600bb1	41600.a	41600bb	$1$	$1$	$ 2^{7} \cdot 5^{2} \cdot 13 $	$ - 2^{13} \cdot 5^{6} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1$	$1$		$0$	$34560$	$0.450775$	$-864/13$	$0.75650$	$2.70077$	$[0, 0, 0, -100, -2000]$	$y^2=x^3-100x-2000$	104.2.0.?	$[ ]$
41600.b1	41600bs1	41600.b	41600bs	$1$	$1$	$ 2^{7} \cdot 5^{2} \cdot 13 $	$ - 2^{7} \cdot 5^{6} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1$	$1$		$0$	$17280$	$0.104202$	$-864/13$	$0.75650$	$2.30974$	$[0, 0, 0, -25, 250]$	$y^2=x^3-25x+250$	104.2.0.?	$[ ]$
41600.ck1	41600o1	41600.ck	41600o	$1$	$1$	$ 2^{7} \cdot 5^{2} \cdot 13 $	$ - 2^{7} \cdot 5^{6} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$10.89707192$	$1$		$0$	$17280$	$0.104202$	$-864/13$	$0.75650$	$2.30974$	$[0, 0, 0, -25, -250]$	$y^2=x^3-25x-250$	104.2.0.?	$[(42526/51, 8081776/51)]$
41600.cl1	41600ba1	41600.cl	41600ba	$1$	$1$	$ 2^{7} \cdot 5^{2} \cdot 13 $	$ - 2^{13} \cdot 5^{6} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1$	$1$		$0$	$34560$	$0.450775$	$-864/13$	$0.75650$	$2.70077$	$[0, 0, 0, -100, 2000]$	$y^2=x^3-100x+2000$	104.2.0.?	$[ ]$
81536.a1	81536o1	81536.a	81536o	$1$	$1$	$ 2^{7} \cdot 7^{2} \cdot 13 $	$ - 2^{7} \cdot 7^{6} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1$	$1$		$0$	$60480$	$0.272438$	$-864/13$	$0.75650$	$2.35082$	$[0, 0, 0, -49, -686]$	$y^2=x^3-49x-686$	104.2.0.?	$[ ]$
81536.b1	81536cl1	81536.b	81536cl	$1$	$1$	$ 2^{7} \cdot 7^{2} \cdot 13 $	$ - 2^{13} \cdot 7^{6} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1$	$1$		$0$	$120960$	$0.619011$	$-864/13$	$0.75650$	$2.71857$	$[0, 0, 0, -196, 5488]$	$y^2=x^3-196x+5488$	104.2.0.?	$[ ]$
81536.ck1	81536by1	81536.ck	81536by	$1$	$1$	$ 2^{7} \cdot 7^{2} \cdot 13 $	$ - 2^{7} \cdot 7^{6} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$6.485378374$	$1$		$0$	$60480$	$0.272438$	$-864/13$	$0.75650$	$2.35082$	$[0, 0, 0, -49, 686]$	$y^2=x^3-49x+686$	104.2.0.?	$[(610/3, 15002/3)]$
81536.cl1	81536ck1	81536.cl	81536ck	$1$	$1$	$ 2^{7} \cdot 7^{2} \cdot 13 $	$ - 2^{13} \cdot 7^{6} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1$	$4$	$2$	$0$	$120960$	$0.619011$	$-864/13$	$0.75650$	$2.71857$	$[0, 0, 0, -196, -5488]$	$y^2=x^3-196x-5488$	104.2.0.?	$[ ]$
194688.g1	194688d1	194688.g	194688d	$1$	$1$	$ 2^{7} \cdot 3^{2} \cdot 13^{2} $	$ - 2^{13} \cdot 3^{6} \cdot 13^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1.322630523$	$1$		$2$	$752640$	$1.477837$	$-864/13$	$0.75650$	$3.37049$	$[0, 0, 0, -6084, 949104]$	$y^2=x^3-6084x+949104$	104.2.0.?	$[(-104, 676)]$
194688.h1	194688e1	194688.h	194688e	$1$	$1$	$ 2^{7} \cdot 3^{2} \cdot 13^{2} $	$ - 2^{13} \cdot 3^{6} \cdot 13^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1.699388366$	$1$		$4$	$752640$	$1.477837$	$-864/13$	$0.75650$	$3.37049$	$[0, 0, 0, -6084, -949104]$	$y^2=x^3-6084x-949104$	104.2.0.?	$[(130, 676)]$
194688.dk1	194688bn1	194688.dk	194688bn	$1$	$1$	$ 2^{7} \cdot 3^{2} \cdot 13^{2} $	$ - 2^{7} \cdot 3^{6} \cdot 13^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$7.103101781$	$1$		$0$	$376320$	$1.131264$	$-864/13$	$0.75650$	$3.02901$	$[0, 0, 0, -1521, 118638]$	$y^2=x^3-1521x+118638$	104.2.0.?	$[(15106/5, 1853254/5)]$
194688.dl1	194688dh1	194688.dl	194688dh	$1$	$1$	$ 2^{7} \cdot 3^{2} \cdot 13^{2} $	$ - 2^{7} \cdot 3^{6} \cdot 13^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1$	$9$	$3$	$0$	$376320$	$1.131264$	$-864/13$	$0.75650$	$3.02901$	$[0, 0, 0, -1521, -118638]$	$y^2=x^3-1521x-118638$	104.2.0.?	$[ ]$
201344.b1	201344be1	201344.b	201344be	$1$	$1$	$ 2^{7} \cdot 11^{2} \cdot 13 $	$ - 2^{13} \cdot 11^{6} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1.011020886$	$1$		$4$	$409600$	$0.845004$	$-864/13$	$0.75650$	$2.73940$	$[0, 0, 0, -484, -21296]$	$y^2=x^3-484x-21296$	104.2.0.?	$[(66, 484)]$
201344.c1	201344bf1	201344.c	201344bf	$1$	$1$	$ 2^{7} \cdot 11^{2} \cdot 13 $	$ - 2^{7} \cdot 11^{6} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1$	$1$		$0$	$204800$	$0.498430$	$-864/13$	$0.75650$	$2.39887$	$[0, 0, 0, -121, 2662]$	$y^2=x^3-121x+2662$	104.2.0.?	$[ ]$
201344.ca1	201344cc1	201344.ca	201344cc	$1$	$1$	$ 2^{7} \cdot 11^{2} \cdot 13 $	$ - 2^{13} \cdot 11^{6} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$3.554372548$	$1$		$0$	$409600$	$0.845004$	$-864/13$	$0.75650$	$2.73940$	$[0, 0, 0, -484, 21296]$	$y^2=x^3-484x+21296$	104.2.0.?	$[(616/3, 15004/3)]$
201344.cd1	201344bd1	201344.cd	201344bd	$1$	$1$	$ 2^{7} \cdot 11^{2} \cdot 13 $	$ - 2^{7} \cdot 11^{6} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$16.06354790$	$1$		$0$	$204800$	$0.498430$	$-864/13$	$0.75650$	$2.39887$	$[0, 0, 0, -121, -2662]$	$y^2=x^3-121x-2662$	104.2.0.?	$[(84879058/1413, 741201786116/1413)]$
374400.ec1	374400ec1	374400.ec	374400ec	$1$	$1$	$ 2^{7} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{13} \cdot 3^{6} \cdot 5^{6} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1$	$1$		$0$	$483840$	$1.000082$	$-864/13$	$0.75650$	$2.75200$	$[0, 0, 0, -900, 54000]$	$y^2=x^3-900x+54000$	104.2.0.?	$[ ]$
374400.ew1	374400ew1	374400.ew	374400ew	$1$	$1$	$ 2^{7} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{7} \cdot 3^{6} \cdot 5^{6} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$7.865364709$	$1$		$0$	$241920$	$0.653508$	$-864/13$	$0.75650$	$2.42792$	$[0, 0, 0, -225, 6750]$	$y^2=x^3-225x+6750$	104.2.0.?	$[(-734/9, 65386/9)]$
374400.gq1	374400gq1	374400.gq	374400gq	$1$	$1$	$ 2^{7} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{7} \cdot 3^{6} \cdot 5^{6} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1$	$1$		$0$	$241920$	$0.653508$	$-864/13$	$0.75650$	$2.42792$	$[0, 0, 0, -225, -6750]$	$y^2=x^3-225x-6750$	104.2.0.?	$[ ]$
374400.hk1	374400hk1	374400.hk	374400hk	$1$	$1$	$ 2^{7} \cdot 3^{2} \cdot 5^{2} \cdot 13 $	$ - 2^{13} \cdot 3^{6} \cdot 5^{6} \cdot 13 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$11.51729858$	$1$		$6$	$483840$	$1.000082$	$-864/13$	$0.75650$	$2.75200$	$[0, 0, 0, -900, -54000]$	$y^2=x^3-900x-54000$	104.2.0.?	$[(46, 44), (64, 388)]$
480896.a1	480896a1	480896.a	480896a	$1$	$1$	$ 2^{7} \cdot 13 \cdot 17^{2} $	$ - 2^{7} \cdot 13 \cdot 17^{6} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1$	$1$		$0$	$704000$	$0.716089$	$-864/13$	$0.75650$	$2.43887$	$[0, 0, 0, -289, 9826]$	$y^2=x^3-289x+9826$	104.2.0.?	$[ ]$
480896.b1	480896b1	480896.b	480896b	$1$	$1$	$ 2^{7} \cdot 13 \cdot 17^{2} $	$ - 2^{13} \cdot 13 \cdot 17^{6} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1$	$1$		$0$	$1408000$	$1.062662$	$-864/13$	$0.75650$	$2.75674$	$[0, 0, 0, -1156, -78608]$	$y^2=x^3-1156x-78608$	104.2.0.?	$[ ]$
480896.be1	480896be1	480896.be	480896be	$1$	$1$	$ 2^{7} \cdot 13 \cdot 17^{2} $	$ - 2^{7} \cdot 13 \cdot 17^{6} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$25.37338336$	$1$		$0$	$704000$	$0.716089$	$-864/13$	$0.75650$	$2.43887$	$[0, 0, 0, -289, -9826]$	$y^2=x^3-289x-9826$	104.2.0.?	$[(71618284258/46311, 13236428078008678/46311)]$
480896.bf1	480896bf1	480896.bf	480896bf	$1$	$1$	$ 2^{7} \cdot 13 \cdot 17^{2} $	$ - 2^{13} \cdot 13 \cdot 17^{6} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$104$	$2$	$0$	$1$	$4$	$2$	$0$	$1408000$	$1.062662$	$-864/13$	$0.75650$	$2.75674$	$[0, 0, 0, -1156, 78608]$	$y^2=x^3-1156x+78608$	104.2.0.?	$[ ]$

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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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