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	Nonmax$\ \ell$	Adelic level	Adelic index	Adelic genus

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Results (26 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	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	Weierstrass coefficients	Weierstrass equation	mod-$m$ images
3192.h4	3192j4	3192.h	3192j	$4$	$4$	$ 2^{3} \cdot 3 \cdot 7 \cdot 19 $	$ - 2^{11} \cdot 3^{4} \cdot 7^{2} \cdot 19^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.59	2B	$456$	$48$	$0$	$1$	$1$		$1$	$5120$	$0.988599$	$55251546334/517244049$	$[0, -1, 0, 1008, 47628]$	$y^2=x^3-x^2+1008x+47628$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.d.1.1, 456.48.0.?
6384.bg4	6384p4	6384.bg	6384p	$4$	$4$	$ 2^{4} \cdot 3 \cdot 7 \cdot 19 $	$ - 2^{11} \cdot 3^{4} \cdot 7^{2} \cdot 19^{4} $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.48	2B	$456$	$48$	$0$	$1$	$1$		$3$	$10240$	$0.988599$	$55251546334/517244049$	$[0, 1, 0, 1008, -47628]$	$y^2=x^3+x^2+1008x-47628$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.d.1.2, 456.48.0.?
9576.e4	9576g4	9576.e	9576g	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 7 \cdot 19 $	$ - 2^{11} \cdot 3^{10} \cdot 7^{2} \cdot 19^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.16	2B	$456$	$48$	$0$	$1$	$1$		$1$	$40960$	$1.537905$	$55251546334/517244049$	$[0, 0, 0, 9069, -1295026]$	$y^2=x^3+9069x-1295026$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.d.1, 12.12.0-4.c.1.1, 24.24.0-8.d.1.1, $\ldots$
19152.h4	19152ba4	19152.h	19152ba	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 7 \cdot 19 $	$ - 2^{11} \cdot 3^{10} \cdot 7^{2} \cdot 19^{4} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.16	2B	$456$	$48$	$0$	$1.121371363$	$1$		$21$	$81920$	$1.537905$	$55251546334/517244049$	$[0, 0, 0, 9069, 1295026]$	$y^2=x^3+9069x+1295026$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.d.1, 12.12.0-4.c.1.2, 24.24.0-8.d.1.2, $\ldots$
22344.r4	22344bj3	22344.r	22344bj	$4$	$4$	$ 2^{3} \cdot 3 \cdot 7^{2} \cdot 19 $	$ - 2^{11} \cdot 3^{4} \cdot 7^{8} \cdot 19^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.16	2B	$3192$	$48$	$0$	$4.114524594$	$1$		$3$	$245760$	$1.961554$	$55251546334/517244049$	$[0, 1, 0, 49376, -16435168]$	$y^2=x^3+x^2+49376x-16435168$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.d.1, 28.12.0-4.c.1.1, 56.24.0-8.d.1.1, $\ldots$
25536.m4	25536ch3	25536.m	25536ch	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 19 $	$ - 2^{17} \cdot 3^{4} \cdot 7^{2} \cdot 19^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.59	2B	$456$	$48$	$0$	$3.185632658$	$1$		$3$	$81920$	$1.335173$	$55251546334/517244049$	$[0, -1, 0, 4031, -385055]$	$y^2=x^3-x^2+4031x-385055$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.d.1.1, 456.48.0.?
25536.ce4	25536bj3	25536.ce	25536bj	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 19 $	$ - 2^{17} \cdot 3^{4} \cdot 7^{2} \cdot 19^{4} $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.48	2B	$456$	$48$	$0$	$1.725750839$	$1$		$11$	$81920$	$1.335173$	$55251546334/517244049$	$[0, 1, 0, 4031, 385055]$	$y^2=x^3+x^2+4031x+385055$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.d.1.2, 456.48.0.?
44688.j4	44688g3	44688.j	44688g	$4$	$4$	$ 2^{4} \cdot 3 \cdot 7^{2} \cdot 19 $	$ - 2^{11} \cdot 3^{4} \cdot 7^{8} \cdot 19^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.16	2B	$3192$	$48$	$0$	$1$	$1$		$1$	$491520$	$1.961554$	$55251546334/517244049$	$[0, -1, 0, 49376, 16435168]$	$y^2=x^3-x^2+49376x+16435168$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.d.1, 28.12.0-4.c.1.2, 56.24.0-8.d.1.2, $\ldots$
60648.bm4	60648o3	60648.bm	60648o	$4$	$4$	$ 2^{3} \cdot 3 \cdot 7 \cdot 19^{2} $	$ - 2^{11} \cdot 3^{4} \cdot 7^{2} \cdot 19^{10} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.16	2B	$456$	$48$	$0$	$10.99165593$	$1$		$1$	$1843200$	$2.460819$	$55251546334/517244049$	$[0, 1, 0, 363768, -328863312]$	$y^2=x^3+x^2+363768x-328863312$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.d.1, 24.24.0-8.d.1.3, 76.12.0.?, $\ldots$
67032.ci4	67032bf3	67032.ci	67032bf	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 19 $	$ - 2^{11} \cdot 3^{10} \cdot 7^{8} \cdot 19^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.16	2B	$3192$	$48$	$0$	$1$	$4$	$2$	$1$	$1966080$	$2.510860$	$55251546334/517244049$	$[0, 0, 0, 444381, 444193918]$	$y^2=x^3+444381x+444193918$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.d.1, 84.12.0.?, 168.24.0.?, $\ldots$
76608.ed4	76608bv3	76608.ed	76608bv	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 19 $	$ - 2^{17} \cdot 3^{10} \cdot 7^{2} \cdot 19^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.16	2B	$456$	$48$	$0$	$2.664036786$	$1$		$5$	$655360$	$1.884478$	$55251546334/517244049$	$[0, 0, 0, 36276, -10360208]$	$y^2=x^3+36276x-10360208$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.d.1, 12.12.0-4.c.1.2, 24.24.0-8.d.1.2, $\ldots$
76608.fd4	76608ey3	76608.fd	76608ey	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 19 $	$ - 2^{17} \cdot 3^{10} \cdot 7^{2} \cdot 19^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.16	2B	$456$	$48$	$0$	$1$	$1$		$1$	$655360$	$1.884478$	$55251546334/517244049$	$[0, 0, 0, 36276, 10360208]$	$y^2=x^3+36276x+10360208$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.d.1, 12.12.0-4.c.1.1, 24.24.0-8.d.1.1, $\ldots$
79800.bn4	79800k3	79800.bn	79800k	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 $	$ - 2^{11} \cdot 3^{4} \cdot 5^{6} \cdot 7^{2} \cdot 19^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.16	2B	$2280$	$48$	$0$	$3.854116680$	$1$		$3$	$655360$	$1.793318$	$55251546334/517244049$	$[0, 1, 0, 25192, 6003888]$	$y^2=x^3+x^2+25192x+6003888$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.d.1, 20.12.0-4.c.1.1, 40.24.0-8.d.1.1, $\ldots$
121296.bq4	121296r3	121296.bq	121296r	$4$	$4$	$ 2^{4} \cdot 3 \cdot 7 \cdot 19^{2} $	$ - 2^{11} \cdot 3^{4} \cdot 7^{2} \cdot 19^{10} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.16	2B	$456$	$48$	$0$	$7.529560293$	$1$		$1$	$3686400$	$2.460819$	$55251546334/517244049$	$[0, -1, 0, 363768, 328863312]$	$y^2=x^3-x^2+363768x+328863312$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.d.1, 24.24.0-8.d.1.3, 76.12.0.?, $\ldots$
134064.er4	134064ex4	134064.er	134064ex	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 19 $	$ - 2^{11} \cdot 3^{10} \cdot 7^{8} \cdot 19^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.16	2B	$3192$	$48$	$0$	$10.98732463$	$1$		$1$	$3932160$	$2.510860$	$55251546334/517244049$	$[0, 0, 0, 444381, -444193918]$	$y^2=x^3+444381x-444193918$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.d.1, 84.12.0.?, 168.24.0.?, $\ldots$
159600.bq4	159600gz4	159600.bq	159600gz	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 $	$ - 2^{11} \cdot 3^{4} \cdot 5^{6} \cdot 7^{2} \cdot 19^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.16	2B	$2280$	$48$	$0$	$1$	$1$		$1$	$1310720$	$1.793318$	$55251546334/517244049$	$[0, -1, 0, 25192, -6003888]$	$y^2=x^3-x^2+25192x-6003888$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.d.1, 20.12.0-4.c.1.2, 40.24.0-8.d.1.2, $\ldots$
178752.ep4	178752kg4	178752.ep	178752kg	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7^{2} \cdot 19 $	$ - 2^{17} \cdot 3^{4} \cdot 7^{8} \cdot 19^{4} $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.16	2B	$3192$	$48$	$0$	$14.25370695$	$1$		$9$	$3932160$	$2.308128$	$55251546334/517244049$	$[0, -1, 0, 197503, -131678847]$	$y^2=x^3-x^2+197503x-131678847$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.d.1, 28.12.0-4.c.1.2, 56.24.0-8.d.1.2, $\ldots$
178752.jd4	178752ce3	178752.jd	178752ce	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7^{2} \cdot 19 $	$ - 2^{17} \cdot 3^{4} \cdot 7^{8} \cdot 19^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.16	2B	$3192$	$48$	$0$	$3.233074325$	$1$		$3$	$3932160$	$2.308128$	$55251546334/517244049$	$[0, 1, 0, 197503, 131678847]$	$y^2=x^3+x^2+197503x+131678847$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.d.1, 28.12.0-4.c.1.1, 56.24.0-8.d.1.1, $\ldots$
181944.j4	181944d3	181944.j	181944d	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 7 \cdot 19^{2} $	$ - 2^{11} \cdot 3^{10} \cdot 7^{2} \cdot 19^{10} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.106	2B	$456$	$48$	$0$	$1$	$4$	$2$	$1$	$14745600$	$3.010124$	$55251546334/517244049$	$[0, 0, 0, 3273909, 8882583334]$	$y^2=x^3+3273909x+8882583334$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.d.1.3, 228.12.0.?, 456.48.0.?
239400.ej4	239400ej4	239400.ej	239400ej	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 $	$ - 2^{11} \cdot 3^{10} \cdot 5^{6} \cdot 7^{2} \cdot 19^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.16	2B	$2280$	$48$	$0$	$1$	$4$	$2$	$1$	$5242880$	$2.342625$	$55251546334/517244049$	$[0, 0, 0, 226725, -161878250]$	$y^2=x^3+226725x-161878250$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.d.1, 60.12.0-4.c.1.1, 120.24.0.?, $\ldots$
363888.r4	363888r4	363888.r	363888r	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 7 \cdot 19^{2} $	$ - 2^{11} \cdot 3^{10} \cdot 7^{2} \cdot 19^{10} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.24.0.106	2B	$456$	$48$	$0$	$1$	$1$		$1$	$29491200$	$3.010124$	$55251546334/517244049$	$[0, 0, 0, 3273909, -8882583334]$	$y^2=x^3+3273909x-8882583334$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.d.1.3, 228.12.0.?, 456.48.0.?
386232.bc4	386232bc4	386232.bc	386232bc	$4$	$4$	$ 2^{3} \cdot 3 \cdot 7 \cdot 11^{2} \cdot 19 $	$ - 2^{11} \cdot 3^{4} \cdot 7^{2} \cdot 11^{6} \cdot 19^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.16	2B	$5016$	$48$	$0$	$1$	$1$		$1$	$6553600$	$2.187546$	$55251546334/517244049$	$[0, -1, 0, 121928, -63880628]$	$y^2=x^3-x^2+121928x-63880628$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.d.1, 44.12.0-4.c.1.1, 88.24.0.?, $\ldots$
424536.h4	424536h3	424536.h	424536h	$4$	$4$	$ 2^{3} \cdot 3 \cdot 7^{2} \cdot 19^{2} $	$ - 2^{11} \cdot 3^{4} \cdot 7^{8} \cdot 19^{10} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.16	2B	$3192$	$48$	$0$	$9.308153622$	$1$		$1$	$88473600$	$3.433773$	$55251546334/517244049$	$[0, -1, 0, 17824616, 112835765260]$	$y^2=x^3-x^2+17824616x+112835765260$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.d.1, 168.24.0.?, 456.24.0.?, $\ldots$
478800.bj4	478800bj3	478800.bj	478800bj	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 $	$ - 2^{11} \cdot 3^{10} \cdot 5^{6} \cdot 7^{2} \cdot 19^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.16	2B	$2280$	$48$	$0$	$0.780730357$	$1$		$9$	$10485760$	$2.342625$	$55251546334/517244049$	$[0, 0, 0, 226725, 161878250]$	$y^2=x^3+226725x+161878250$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.d.1, 60.12.0-4.c.1.2, 120.24.0.?, $\ldots$
485184.q4	485184q4	485184.q	485184q	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 19^{2} $	$ - 2^{17} \cdot 3^{4} \cdot 7^{2} \cdot 19^{10} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.16	2B	$456$	$48$	$0$	$1$	$1$		$1$	$29491200$	$2.807392$	$55251546334/517244049$	$[0, -1, 0, 1455071, -2632361567]$	$y^2=x^3-x^2+1455071x-2632361567$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.d.1, 24.24.0-8.d.1.4, 76.12.0.?, $\ldots$
485184.fq4	485184fq3	485184.fq	485184fq	$4$	$4$	$ 2^{6} \cdot 3 \cdot 7 \cdot 19^{2} $	$ - 2^{17} \cdot 3^{4} \cdot 7^{2} \cdot 19^{10} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.16	2B	$456$	$48$	$0$	$2.241399253$	$1$		$5$	$29491200$	$2.807392$	$55251546334/517244049$	$[0, 1, 0, 1455071, 2632361567]$	$y^2=x^3+x^2+1455071x+2632361567$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.d.1, 24.24.0-8.d.1.4, 76.12.0.?, $\ldots$

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Classical	Maass
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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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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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