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

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Results (20 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	Semistable	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
2093.d1	2093d2	2093.d	2093d	$2$	$2$	$ 7 \cdot 13 \cdot 23 $	$ 7^{2} \cdot 13^{4} \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	2.3.0.1	2B	$644$	$12$	$0$	$1$	$1$	$0$	$480$	$0.145152$	$104154702625/32188247$	$0.84011$	$3.31781$	$[1, 1, 1, -98, -296]$	$y^2+xy+y=x^3+x^2-98x-296$	2.3.0.a.1, 28.6.0.c.1, 92.6.0.?, 644.12.0.?	$[]$
14651.d1	14651l2	14651.d	14651l	$2$	$2$	$ 7^{2} \cdot 13 \cdot 23 $	$ 7^{8} \cdot 13^{4} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$644$	$12$	$0$	$0.442068241$	$1$	$8$	$23040$	$1.118107$	$104154702625/32188247$	$0.84011$	$3.86193$	$[1, 0, 0, -4803, 87058]$	$y^2+xy=x^3-4803x+87058$	2.3.0.a.1, 28.6.0.c.1, 92.6.0.?, 644.12.0.?	$[(-3, 320)]$
18837.l1	18837j2	18837.l	18837j	$2$	$2$	$ 3^{2} \cdot 7 \cdot 13 \cdot 23 $	$ 3^{6} \cdot 7^{2} \cdot 13^{4} \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$644$	$12$	$0$	$1$	$1$	$0$	$11520$	$0.694458$	$104154702625/32188247$	$0.84011$	$3.24687$	$[1, -1, 0, -882, 7105]$	$y^2+xy=x^3-x^2-882x+7105$	2.3.0.a.1, 28.6.0.c.1, 92.6.0.?, 644.12.0.?	$[]$
27209.m1	27209e2	27209.m	27209e	$2$	$2$	$ 7 \cdot 13^{2} \cdot 23 $	$ 7^{2} \cdot 13^{10} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$644$	$12$	$0$	$10.80654990$	$1$	$0$	$80640$	$1.427626$	$104154702625/32188247$	$0.84011$	$3.99154$	$[1, 1, 0, -16565, -567094]$	$y^2+xy=x^3+x^2-16565x-567094$	2.3.0.a.1, 28.6.0.c.1, 92.6.0.?, 644.12.0.?	$[(6016366/183, 8734826416/183)]$
33488.e1	33488n2	33488.e	33488n	$2$	$2$	$ 2^{4} \cdot 7 \cdot 13 \cdot 23 $	$ 2^{12} \cdot 7^{2} \cdot 13^{4} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$644$	$12$	$0$	$1.996182655$	$1$	$5$	$30720$	$0.838299$	$104154702625/32188247$	$0.84011$	$3.23324$	$[0, 1, 0, -1568, 15796]$	$y^2=x^3+x^2-1568x+15796$	2.3.0.a.1, 28.6.0.c.1, 92.6.0.?, 644.12.0.?	$[(4, 98)]$
48139.e1	48139c2	48139.e	48139c	$2$	$2$	$ 7 \cdot 13 \cdot 23^{2} $	$ 7^{2} \cdot 13^{4} \cdot 23^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$644$	$12$	$0$	$1$	$1$	$0$	$253440$	$1.712898$	$104154702625/32188247$	$0.84011$	$4.09782$	$[1, 1, 1, -51853, 3080740]$	$y^2+xy+y=x^3+x^2-51853x+3080740$	2.3.0.a.1, 28.6.0.c.1, 92.6.0.?, 644.12.0.?	$[]$
52325.k1	52325h2	52325.k	52325h	$2$	$2$	$ 5^{2} \cdot 7 \cdot 13 \cdot 23 $	$ 5^{6} \cdot 7^{2} \cdot 13^{4} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$644$	$12$	$0$	$1.005740393$	$1$	$4$	$69120$	$0.949871$	$104154702625/32188247$	$0.84011$	$3.22366$	$[1, 0, 1, -2451, -32077]$	$y^2+xy+y=x^3-2451x-32077$	2.3.0.a.1, 28.6.0.c.1, 92.6.0.?, 644.12.0.?	$[(67, 291)]$
131859.bd1	131859bc2	131859.bd	131859bc	$2$	$2$	$ 3^{2} \cdot 7^{2} \cdot 13 \cdot 23 $	$ 3^{6} \cdot 7^{8} \cdot 13^{4} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$644$	$12$	$0$	$3.460149123$	$1$	$2$	$552960$	$1.667414$	$104154702625/32188247$	$0.84011$	$3.70129$	$[1, -1, 0, -43227, -2350566]$	$y^2+xy=x^3-x^2-43227x-2350566$	2.3.0.a.1, 28.6.0.c.1, 92.6.0.?, 644.12.0.?	$[(3922, 243284)]$
133952.o1	133952bt2	133952.o	133952bt	$2$	$2$	$ 2^{6} \cdot 7 \cdot 13 \cdot 23 $	$ 2^{18} \cdot 7^{2} \cdot 13^{4} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$644$	$12$	$0$	$1.236640837$	$1$	$7$	$245760$	$1.184872$	$104154702625/32188247$	$0.84011$	$3.20585$	$[0, 1, 0, -6273, -132641]$	$y^2=x^3+x^2-6273x-132641$	2.3.0.a.1, 28.6.0.c.1, 92.6.0.?, 644.12.0.?	$[(-37, 224)]$
133952.cm1	133952bj2	133952.cm	133952bj	$2$	$2$	$ 2^{6} \cdot 7 \cdot 13 \cdot 23 $	$ 2^{18} \cdot 7^{2} \cdot 13^{4} \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$644$	$12$	$0$	$1$	$1$	$1$	$245760$	$1.184872$	$104154702625/32188247$	$0.84011$	$3.20585$	$[0, -1, 0, -6273, 132641]$	$y^2=x^3-x^2-6273x+132641$	2.3.0.a.1, 28.6.0.c.1, 92.6.0.?, 644.12.0.?	$[]$
190463.bg1	190463bg2	190463.bg	190463bg	$2$	$2$	$ 7^{2} \cdot 13^{2} \cdot 23 $	$ 7^{8} \cdot 13^{10} \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$644$	$12$	$0$	$1$	$1$	$0$	$3870720$	$2.400581$	$104154702625/32188247$	$0.84011$	$4.31302$	$[1, 0, 1, -811711, 192078135]$	$y^2+xy+y=x^3-811711x+192078135$	2.3.0.a.1, 28.6.0.c.1, 92.6.0.?, 644.12.0.?	$[]$
234416.bw1	234416bw2	234416.bw	234416bw	$2$	$2$	$ 2^{4} \cdot 7^{2} \cdot 13 \cdot 23 $	$ 2^{12} \cdot 7^{8} \cdot 13^{4} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$644$	$12$	$0$	$5.176344150$	$1$	$1$	$1474560$	$1.811255$	$104154702625/32188247$	$0.84011$	$3.66865$	$[0, -1, 0, -76848, -5571712]$	$y^2=x^3-x^2-76848x-5571712$	2.3.0.a.1, 28.6.0.c.1, 92.6.0.?, 644.12.0.?	$[(5218/3, 324478/3)]$
244881.s1	244881s2	244881.s	244881s	$2$	$2$	$ 3^{2} \cdot 7 \cdot 13^{2} \cdot 23 $	$ 3^{6} \cdot 7^{2} \cdot 13^{10} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$644$	$12$	$0$	$1.495929755$	$1$	$6$	$1935360$	$1.976933$	$104154702625/32188247$	$0.84011$	$3.81597$	$[1, -1, 1, -149090, 15162450]$	$y^2+xy+y=x^3-x^2-149090x+15162450$	2.3.0.a.1, 28.6.0.c.1, 92.6.0.?, 644.12.0.?	$[(-94, 5370)]$
253253.n1	253253n2	253253.n	253253n	$2$	$2$	$ 7 \cdot 11^{2} \cdot 13 \cdot 23 $	$ 7^{2} \cdot 11^{6} \cdot 13^{4} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$644$	$12$	$0$	$2.074099171$	$1$	$2$	$614400$	$1.344099$	$104154702625/32188247$	$0.84011$	$3.19531$	$[1, 1, 0, -11860, 334437]$	$y^2+xy=x^3+x^2-11860x+334437$	2.3.0.a.1, 28.6.0.c.1, 92.6.0.?, 644.12.0.?	$[(204, 2439)]$
301392.bl1	301392bl2	301392.bl	301392bl	$2$	$2$	$ 2^{4} \cdot 3^{2} \cdot 7 \cdot 13 \cdot 23 $	$ 2^{12} \cdot 3^{6} \cdot 7^{2} \cdot 13^{4} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$644$	$12$	$0$	$2.032490366$	$1$	$7$	$737280$	$1.387606$	$104154702625/32188247$	$0.84011$	$3.19262$	$[0, 0, 0, -14115, -440606]$	$y^2=x^3-14115x-440606$	2.3.0.a.1, 28.6.0.c.1, 92.6.0.?, 644.12.0.?	$[(135, 338)]$
336973.e1	336973e2	336973.e	336973e	$2$	$2$	$ 7^{2} \cdot 13 \cdot 23^{2} $	$ 7^{8} \cdot 13^{4} \cdot 23^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$644$	$12$	$0$	$1$	$1$	$0$	$12165120$	$2.685856$	$104154702625/32188247$	$0.84011$	$4.38864$	$[1, 0, 0, -2540798, -1064316275]$	$y^2+xy=x^3-2540798x-1064316275$	2.3.0.a.1, 28.6.0.c.1, 92.6.0.?, 644.12.0.?	$[]$
366275.bh1	366275bh2	366275.bh	366275bh	$2$	$2$	$ 5^{2} \cdot 7^{2} \cdot 13 \cdot 23 $	$ 5^{6} \cdot 7^{8} \cdot 13^{4} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$644$	$12$	$0$	$8.959155381$	$1$	$0$	$3317760$	$1.922827$	$104154702625/32188247$	$0.84011$	$3.64536$	$[1, 1, 0, -120075, 10882250]$	$y^2+xy=x^3+x^2-120075x+10882250$	2.3.0.a.1, 28.6.0.c.1, 92.6.0.?, 644.12.0.?	$[(-179005/22, 25474355/22)]$
433251.bh1	433251bh2	433251.bh	433251bh	$2$	$2$	$ 3^{2} \cdot 7 \cdot 13 \cdot 23^{2} $	$ 3^{6} \cdot 7^{2} \cdot 13^{4} \cdot 23^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$644$	$12$	$0$	$4.015596358$	$1$	$0$	$6082560$	$2.262203$	$104154702625/32188247$	$0.84011$	$3.91197$	$[1, -1, 0, -466677, -83646662]$	$y^2+xy=x^3-x^2-466677x-83646662$	2.3.0.a.1, 28.6.0.c.1, 92.6.0.?, 644.12.0.?	$[(-2253/2, 6485/2)]$
435344.i1	435344i2	435344.i	435344i	$2$	$2$	$ 2^{4} \cdot 7 \cdot 13^{2} \cdot 23 $	$ 2^{12} \cdot 7^{2} \cdot 13^{10} \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$644$	$12$	$0$	$1$	$1$	$1$	$5160960$	$2.120773$	$104154702625/32188247$	$0.84011$	$3.77981$	$[0, 1, 0, -265048, 35763924]$	$y^2=x^3+x^2-265048x+35763924$	2.3.0.a.1, 28.6.0.c.1, 92.6.0.?, 644.12.0.?	$[]$
470925.y1	470925y2	470925.y	470925y	$2$	$2$	$ 3^{2} \cdot 5^{2} \cdot 7 \cdot 13 \cdot 23 $	$ 3^{6} \cdot 5^{6} \cdot 7^{2} \cdot 13^{4} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	2.3.0.1	2B	$644$	$12$	$0$	$1.497832628$	$1$	$6$	$1658880$	$1.499176$	$104154702625/32188247$	$0.84011$	$3.18604$	$[1, -1, 1, -22055, 866072]$	$y^2+xy+y=x^3-x^2-22055x+866072$	2.3.0.a.1, 28.6.0.c.1, 92.6.0.?, 644.12.0.?	$[(124, 100)]$

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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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