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 (22 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	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
9240.bi5	9240bj1	9240.bi	9240bj	$6$	$8$	$ 2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 3^{16} \cdot 5^{2} \cdot 7^{2} \cdot 11 $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.32	2B	$1232$	$192$	$1$	$1.318078638$	$1$		$9$	$16384$	$1.169926$	$84611246065664/580054565475$	$0.97880$	$4.07669$	$[0, 1, 0, 2305, 141018]$	$y^2=x^3+x^2+2305x+141018$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 16.48.0-16.e.2.7, 22.6.0.a.1, $\ldots$	$[(-29, 225)]$
18480.bf5	18480m1	18480.bf	18480m	$6$	$8$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 3^{16} \cdot 5^{2} \cdot 7^{2} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.48	2B	$1232$	$192$	$1$	$5.859454812$	$1$		$1$	$32768$	$1.169926$	$84611246065664/580054565475$	$0.97880$	$3.78907$	$[0, -1, 0, 2305, -141018]$	$y^2=x^3-x^2+2305x-141018$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 16.48.0-16.e.2.5, 22.6.0.a.1, $\ldots$	$[(406/3, 6200/3)]$
27720.u5	27720k1	27720.u	27720k	$6$	$8$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 3^{22} \cdot 5^{2} \cdot 7^{2} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.24.0.13	2B	$3696$	$192$	$1$	$1$	$1$		$1$	$131072$	$1.719231$	$84611246065664/580054565475$	$0.97880$	$4.28324$	$[0, 0, 0, 20742, -3786743]$	$y^2=x^3+20742x-3786743$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 12.12.0-4.c.1.2, 16.24.0.e.2, $\ldots$	$[]$
46200.e5	46200a1	46200.e	46200a	$6$	$8$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 3^{16} \cdot 5^{8} \cdot 7^{2} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.24.0.13	2B	$6160$	$192$	$1$	$2.615149506$	$1$		$3$	$393216$	$1.974644$	$84611246065664/580054565475$	$0.97880$	$4.36489$	$[0, -1, 0, 57617, 17512012]$	$y^2=x^3-x^2+57617x+17512012$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.e.2, 20.12.0-4.c.1.2, $\ldots$	$[(-168, 1750)]$
55440.m5	55440h1	55440.m	55440h	$6$	$8$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 3^{22} \cdot 5^{2} \cdot 7^{2} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.24.0.13	2B	$3696$	$192$	$1$	$1$	$1$		$1$	$262144$	$1.719231$	$84611246065664/580054565475$	$0.97880$	$4.01144$	$[0, 0, 0, 20742, 3786743]$	$y^2=x^3+20742x+3786743$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 12.12.0-4.c.1.1, 16.24.0.e.2, $\ldots$	$[]$
64680.f5	64680bh1	64680.f	64680bh	$6$	$8$	$ 2^{3} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{4} \cdot 3^{16} \cdot 5^{2} \cdot 7^{8} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.166	2B	$1232$	$192$	$1$	$9.756460724$	$1$		$1$	$786432$	$2.142879$	$84611246065664/580054565475$	$0.97880$	$4.41456$	$[0, -1, 0, 112929, -48143304]$	$y^2=x^3-x^2+112929x-48143304$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.5, 16.48.0-16.e.2.4, 22.6.0.a.1, $\ldots$	$[(84577/17, 15446613/17)]$
73920.bw5	73920o1	73920.bw	73920o	$6$	$8$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{10} \cdot 3^{16} \cdot 5^{2} \cdot 7^{2} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.194	2B	$1232$	$192$	$1$	$3.436934999$	$1$		$3$	$262144$	$1.516499$	$84611246065664/580054565475$	$0.97880$	$3.69150$	$[0, -1, 0, 9219, 1118925]$	$y^2=x^3-x^2+9219x+1118925$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.11, 16.48.0-16.e.2.6, 22.6.0.a.1, $\ldots$	$[(-11, 1008)]$
73920.ep5	73920ge1	73920.ep	73920ge	$6$	$8$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{10} \cdot 3^{16} \cdot 5^{2} \cdot 7^{2} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.185	2B	$1232$	$192$	$1$	$0.766756063$	$1$		$7$	$262144$	$1.516499$	$84611246065664/580054565475$	$0.97880$	$3.69150$	$[0, 1, 0, 9219, -1118925]$	$y^2=x^3+x^2+9219x-1118925$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.9, 16.48.0-16.e.2.8, 22.6.0.a.1, $\ldots$	$[(102, 945)]$
92400.ic5	92400cm1	92400.ic	92400cm	$6$	$8$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 3^{16} \cdot 5^{8} \cdot 7^{2} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.24.0.13	2B	$6160$	$192$	$1$	$1$	$1$		$1$	$786432$	$1.974644$	$84611246065664/580054565475$	$0.97880$	$4.10028$	$[0, 1, 0, 57617, -17512012]$	$y^2=x^3+x^2+57617x-17512012$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.e.2, 20.12.0-4.c.1.1, $\ldots$	$[]$
101640.cl5	101640bg1	101640.cl	101640bg	$6$	$8$	$ 2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} $	$ - 2^{4} \cdot 3^{16} \cdot 5^{2} \cdot 7^{2} \cdot 11^{7} $	$0$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.38	2B	$1232$	$192$	$1$	$1$	$1$		$3$	$1966080$	$2.368874$	$84611246065664/580054565475$	$0.97880$	$4.47671$	$[0, 1, 0, 278865, -186579450]$	$y^2=x^3+x^2+278865x-186579450$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.12, 16.48.0-16.e.2.10, 22.6.0.a.1, $\ldots$	$[]$
129360.fk5	129360cb1	129360.fk	129360cb	$6$	$8$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{4} \cdot 3^{16} \cdot 5^{2} \cdot 7^{8} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.94	2B	$1232$	$192$	$1$	$1$	$1$		$1$	$1572864$	$2.142879$	$84611246065664/580054565475$	$0.97880$	$4.15459$	$[0, 1, 0, 112929, 48143304]$	$y^2=x^3+x^2+112929x+48143304$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.1, 16.48.0-16.e.2.2, 22.6.0.a.1, $\ldots$	$[]$
138600.cf5	138600bs1	138600.cf	138600bs	$6$	$8$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 3^{22} \cdot 5^{8} \cdot 7^{2} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.24.0.13	2B	$18480$	$192$	$1$	$1$	$1$		$1$	$3145728$	$2.523949$	$84611246065664/580054565475$	$0.97880$	$4.51662$	$[0, 0, 0, 518550, -473342875]$	$y^2=x^3+518550x-473342875$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.e.2, 22.6.0.a.1, $\ldots$	$[]$
194040.eu5	194040ch1	194040.eu	194040ch	$6$	$8$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{4} \cdot 3^{22} \cdot 5^{2} \cdot 7^{8} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.24.0.13	2B	$3696$	$192$	$1$	$8.844731830$	$1$		$1$	$6291456$	$2.692184$	$84611246065664/580054565475$	$0.97880$	$4.55761$	$[0, 0, 0, 1016358, 1298852849]$	$y^2=x^3+1016358x+1298852849$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.e.2, 22.6.0.a.1, $\ldots$	$[(-36463/8, 11841095/8)]$
203280.dl5	203280gc1	203280.dl	203280gc	$6$	$8$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} $	$ - 2^{4} \cdot 3^{16} \cdot 5^{2} \cdot 7^{2} \cdot 11^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.54	2B	$1232$	$192$	$1$	$1$	$4$	$2$	$1$	$3932160$	$2.368874$	$84611246065664/580054565475$	$0.97880$	$4.22283$	$[0, -1, 0, 278865, 186579450]$	$y^2=x^3-x^2+278865x+186579450$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.10, 16.48.0-16.e.2.12, 22.6.0.a.1, $\ldots$	$[]$
221760.jr5	221760cd1	221760.jr	221760cd	$6$	$8$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{10} \cdot 3^{22} \cdot 5^{2} \cdot 7^{2} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.24.0.13	2B	$3696$	$192$	$1$	$5.532885164$	$1$		$3$	$2097152$	$2.065804$	$84611246065664/580054565475$	$0.97880$	$3.89753$	$[0, 0, 0, 82968, 30293944]$	$y^2=x^3+82968x+30293944$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.e.2, 22.6.0.a.1, $\ldots$	$[(30, 5728)]$
221760.mc5	221760iw1	221760.mc	221760iw	$6$	$8$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ - 2^{10} \cdot 3^{22} \cdot 5^{2} \cdot 7^{2} \cdot 11 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.24.0.13	2B	$3696$	$192$	$1$	$1$	$4$	$2$	$1$	$2097152$	$2.065804$	$84611246065664/580054565475$	$0.97880$	$3.89753$	$[0, 0, 0, 82968, -30293944]$	$y^2=x^3+82968x-30293944$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.e.2, 22.6.0.a.1, $\ldots$	$[]$
277200.jn5	277200jn1	277200.jn	277200jn	$6$	$8$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{4} \cdot 3^{22} \cdot 5^{8} \cdot 7^{2} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.24.0.13	2B	$18480$	$192$	$1$	$7.290445703$	$1$		$1$	$6291456$	$2.523949$	$84611246065664/580054565475$	$0.97880$	$4.26681$	$[0, 0, 0, 518550, 473342875]$	$y^2=x^3+518550x+473342875$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.e.2, 22.6.0.a.1, $\ldots$	$[(-6015/4, 960575/4)]$
304920.s5	304920s1	304920.s	304920s	$6$	$8$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11^{2} $	$ - 2^{4} \cdot 3^{22} \cdot 5^{2} \cdot 7^{2} \cdot 11^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.24.0.13	2B	$3696$	$192$	$1$	$1$	$1$		$1$	$15728640$	$2.918179$	$84611246065664/580054565475$	$0.97880$	$4.60924$	$[0, 0, 0, 2509782, 5040154933]$	$y^2=x^3+2509782x+5040154933$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 12.12.0-4.c.1.2, 16.24.0.e.2, $\ldots$	$[]$
323400.fu5	323400fu1	323400.fu	323400fu	$6$	$8$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 11 $	$ - 2^{4} \cdot 3^{16} \cdot 5^{8} \cdot 7^{8} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.24.0.13	2B	$6160$	$192$	$1$	$2.417500645$	$1$		$5$	$18874368$	$2.947598$	$84611246065664/580054565475$	$0.97880$	$4.61569$	$[0, 1, 0, 2823217, -6012266562]$	$y^2=x^3+x^2+2823217x-6012266562$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.e.2, 22.6.0.a.1, $\ldots$	$[(2053, 91875)]$
369600.ho5	369600ho1	369600.ho	369600ho	$6$	$8$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{10} \cdot 3^{16} \cdot 5^{8} \cdot 7^{2} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.24.0.13	2B	$6160$	$192$	$1$	$6.638672410$	$1$		$1$	$6291456$	$2.321217$	$84611246065664/580054565475$	$0.97880$	$3.98130$	$[0, -1, 0, 230467, -140326563]$	$y^2=x^3-x^2+230467x-140326563$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.e.2, 22.6.0.a.1, $\ldots$	$[(8733/2, 830025/2)]$
369600.pi5	369600pi1	369600.pi	369600pi	$6$	$8$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 $	$ - 2^{10} \cdot 3^{16} \cdot 5^{8} \cdot 7^{2} \cdot 11 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.24.0.13	2B	$6160$	$192$	$1$	$0.990843871$	$1$		$7$	$6291456$	$2.321217$	$84611246065664/580054565475$	$0.97880$	$3.98130$	$[0, 1, 0, 230467, 140326563]$	$y^2=x^3+x^2+230467x+140326563$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.e.2, 22.6.0.a.1, $\ldots$	$[(163, 13500)]$
388080.jy5	388080jy1	388080.jy	388080jy	$6$	$8$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ - 2^{4} \cdot 3^{22} \cdot 5^{2} \cdot 7^{8} \cdot 11 $	$2$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.24.0.13	2B	$3696$	$192$	$1$	$53.97569385$	$1$		$5$	$12582912$	$2.692184$	$84611246065664/580054565475$	$0.97880$	$4.31213$	$[0, 0, 0, 1016358, -1298852849]$	$y^2=x^3+1016358x-1298852849$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.e.2, 22.6.0.a.1, $\ldots$	$[(1575, 64876), (196273/12, 88426135/12)]$

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Classical	Maass
Hilbert	Bianchi

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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