LMFDB - Elliptic curves over $\Q$ of conductor 3900

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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 (23 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
3900.a1	3900c4	3900.a	3900c	$4$	$6$	$ 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{8} \cdot 3 \cdot 5^{6} \cdot 13^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$780$	$96$	$1$	$1$	$1$	$1$	$10368$	$1.384178$	$181037698000/14480427$	$0.98201$	$4.97341$	$[0, -1, 0, -18708, -908088]$	$y^2=x^3-x^2-18708x-908088$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.h.1, 15.8.0-3.a.1.1, $\ldots$	$[]$
3900.a2	3900c3	3900.a	3900c	$4$	$6$	$ 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{4} \cdot 3^{2} \cdot 5^{6} \cdot 13^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$780$	$96$	$1$	$1$	$1$	$1$	$5184$	$1.037603$	$2725888000000/19773$	$1.18802$	$4.96606$	$[0, -1, 0, -18333, -949338]$	$y^2=x^3-x^2-18333x-949338$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 15.8.0-3.a.1.1, $\ldots$	$[]$
3900.a3	3900c2	3900.a	3900c	$4$	$6$	$ 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{8} \cdot 3^{3} \cdot 5^{6} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$780$	$96$	$1$	$1$	$1$	$1$	$3456$	$0.834871$	$1409938000/4563$	$0.93342$	$4.38624$	$[0, -1, 0, -3708, 87912]$	$y^2=x^3-x^2-3708x+87912$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.h.1, 15.8.0-3.a.1.2, $\ldots$	$[]$
3900.a4	3900c1	3900.a	3900c	$4$	$6$	$ 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{4} \cdot 3^{6} \cdot 5^{6} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$780$	$96$	$1$	$1$	$1$	$1$	$1728$	$0.488297$	$16384000/9477$	$1.48887$	$3.51215$	$[0, -1, 0, -333, 162]$	$y^2=x^3-x^2-333x+162$	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.i.1, 15.8.0-3.a.1.2, $\ldots$	$[]$
3900.b1	3900b1	3900.b	3900b	$2$	$3$	$ 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 $	$ - 2^{8} \cdot 3^{12} \cdot 5^{2} \cdot 13^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$780$	$16$	$0$	$1$	$1$	$0$	$5184$	$1.151520$	$-74605986640/1167575877$	$0.99796$	$4.49081$	$[0, -1, 0, -1628, 134472]$	$y^2=x^3-x^2-1628x+134472$	3.4.0.a.1, 15.8.0-3.a.1.2, 52.2.0.a.1, 156.8.0.?, 780.16.0.?	$[]$
3900.b2	3900b2	3900.b	3900b	$2$	$3$	$ 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 $	$ - 2^{8} \cdot 3^{4} \cdot 5^{2} \cdot 13^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$780$	$16$	$0$	$1$	$1$	$0$	$15552$	$1.700825$	$53465227872560/858964449213$	$1.03397$	$5.28026$	$[0, -1, 0, 14572, -3507288]$	$y^2=x^3-x^2+14572x-3507288$	3.4.0.a.1, 15.8.0-3.a.1.1, 52.2.0.a.1, 156.8.0.?, 780.16.0.?	$[]$
3900.c1	3900e1	3900.c	3900e	$1$	$1$	$ 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 $	$ - 2^{8} \cdot 3 \cdot 5^{3} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$390$	$2$	$0$	$0.192753106$	$1$	$6$	$672$	$-0.081479$	$-524288/39$	$0.93878$	$2.86189$	$[0, -1, 0, -53, 177]$	$y^2=x^3-x^2-53x+177$	390.2.0.?	$[(7, 10)]$
3900.d1	3900a2	3900.d	3900a	$2$	$3$	$ 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 $	$ - 2^{8} \cdot 3 \cdot 5^{9} \cdot 13^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$390$	$16$	$0$	$1$	$1$	$0$	$5184$	$1.127720$	$-4684079104/823875$	$0.93879$	$4.56353$	$[0, -1, 0, -5533, -179063]$	$y^2=x^3-x^2-5533x-179063$	3.4.0.a.1, 15.8.0-3.a.1.1, 78.8.0.?, 390.16.0.?	$[]$
3900.d2	3900a1	3900.d	3900a	$2$	$3$	$ 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 $	$ - 2^{8} \cdot 3^{3} \cdot 5^{7} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$390$	$16$	$0$	$1$	$1$	$0$	$1728$	$0.578413$	$2809856/1755$	$0.89795$	$3.63423$	$[0, -1, 0, 467, 937]$	$y^2=x^3-x^2+467x+937$	3.4.0.a.1, 15.8.0-3.a.1.2, 78.8.0.?, 390.16.0.?	$[]$
3900.e1	3900d1	3900.e	3900d	$2$	$2$	$ 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{4} \cdot 3^{8} \cdot 5^{8} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$520$	$48$	$0$	$3.957653191$	$1$	$3$	$4608$	$0.939837$	$3718856704/2132325$	$1.07236$	$4.16822$	$[0, -1, 0, -2033, 4062]$	$y^2=x^3-x^2-2033x+4062$	2.3.0.a.1, 4.6.0.b.1, 26.6.0.b.1, 40.12.0-4.b.1.2, 52.12.0.e.1, $\ldots$	$[(-14, 172)]$
3900.e2	3900d2	3900.e	3900d	$2$	$2$	$ 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 $	$ - 2^{8} \cdot 3^{4} \cdot 5^{10} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.5	2B	$520$	$48$	$0$	$1.978826595$	$1$	$3$	$9216$	$1.286411$	$14647977776/8555625$	$0.99143$	$4.66932$	$[0, -1, 0, 8092, 24312]$	$y^2=x^3-x^2+8092x+24312$	2.3.0.a.1, 4.6.0.a.1, 40.12.0-4.a.1.1, 52.12.0.d.1, 104.24.0.?, $\ldots$	$[(497, 11250)]$
3900.f1	3900f1	3900.f	3900f	$1$	$1$	$ 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 $	$ - 2^{8} \cdot 3^{4} \cdot 5^{8} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$52$	$2$	$0$	$1$	$1$	$0$	$2880$	$0.838832$	$-5513680/1053$	$0.80478$	$4.13952$	$[0, -1, 0, -1708, 31912]$	$y^2=x^3-x^2-1708x+31912$	52.2.0.a.1	$[]$
3900.g1	3900g1	3900.g	3900g	$1$	$1$	$ 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 $	$ - 2^{8} \cdot 3^{5} \cdot 5^{3} \cdot 13^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$390$	$2$	$0$	$1$	$1$	$0$	$16800$	$1.611307$	$-769623354048512/15247889631$	$1.07815$	$5.40398$	$[0, -1, 0, -60613, -5821103]$	$y^2=x^3-x^2-60613x-5821103$	390.2.0.?	$[]$
3900.h1	3900j1	3900.h	3900j	$1$	$1$	$ 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 $	$ - 2^{8} \cdot 3^{4} \cdot 5^{2} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$52$	$2$	$0$	$0.145448002$	$1$	$8$	$576$	$0.034113$	$-5513680/1053$	$0.80478$	$2.97168$	$[0, 1, 0, -68, 228]$	$y^2=x^3+x^2-68x+228$	52.2.0.a.1	$[(4, 6)]$
3900.i1	3900i1	3900.i	3900i	$1$	$1$	$ 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 $	$ - 2^{8} \cdot 3^{13} \cdot 5^{11} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$390$	$2$	$0$	$0.177846173$	$1$	$8$	$37440$	$2.020226$	$3186827264/64769371875$	$1.15762$	$5.75065$	$[0, 1, 0, 4867, -24487137]$	$y^2=x^3+x^2+4867x-24487137$	390.2.0.?	$[(2173, 101250)]$
3900.j1	3900l1	3900.j	3900l	$1$	$1$	$ 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 $	$ - 2^{8} \cdot 3^{5} \cdot 5^{9} \cdot 13^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$390$	$2$	$0$	$1$	$1$	$0$	$84000$	$2.416027$	$-769623354048512/15247889631$	$1.07815$	$6.57183$	$[0, 1, 0, -1515333, -730668537]$	$y^2=x^3+x^2-1515333x-730668537$	390.2.0.?	$[]$
3900.k1	3900n1	3900.k	3900n	$1$	$1$	$ 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 $	$ - 2^{8} \cdot 3 \cdot 5^{9} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$390$	$2$	$0$	$1.692976881$	$1$	$2$	$3360$	$0.723240$	$-524288/39$	$0.93878$	$4.02974$	$[0, 1, 0, -1333, 19463]$	$y^2=x^3+x^2-1333x+19463$	390.2.0.?	$[(58, 375)]$
3900.l1	3900m1	3900.l	3900m	$2$	$3$	$ 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 $	$ - 2^{8} \cdot 3^{12} \cdot 5^{8} \cdot 13^{3} $	$1$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.1	3B.1.1	$156$	$16$	$0$	$0.404858286$	$1$	$16$	$25920$	$1.956238$	$-74605986640/1167575877$	$0.99796$	$5.65866$	$[0, 1, 0, -40708, 16727588]$	$y^2=x^3+x^2-40708x+16727588$	3.8.0-3.a.1.2, 52.2.0.a.1, 156.16.0.?	$[(332, 6318)]$
3900.l2	3900m2	3900.l	3900m	$2$	$3$	$ 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 $	$ - 2^{8} \cdot 3^{4} \cdot 5^{8} \cdot 13^{9} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.2	3B.1.2	$156$	$16$	$0$	$1.214574860$	$1$	$2$	$77760$	$2.505543$	$53465227872560/858964449213$	$1.03397$	$6.44811$	$[0, 1, 0, 364292, -437682412]$	$y^2=x^3+x^2+364292x-437682412$	3.8.0-3.a.1.1, 52.2.0.a.1, 156.16.0.?	$[(707, 13182)]$
3900.m1	3900h2	3900.m	3900h	$2$	$2$	$ 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{8} \cdot 3 \cdot 5^{6} \cdot 13^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$4.250394424$	$1$	$1$	$1920$	$0.512193$	$3631696/507$	$0.85077$	$3.66526$	$[0, 1, 0, -508, -4012]$	$y^2=x^3+x^2-508x-4012$	2.3.0.a.1, 12.6.0.a.1, 52.6.0.c.1, 156.12.0.?	$[(-59/2, 177/2)]$
3900.m2	3900h1	3900.m	3900h	$2$	$2$	$ 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{4} \cdot 3^{2} \cdot 5^{6} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$2.125197212$	$1$	$3$	$960$	$0.165619$	$1048576/117$	$1.06619$	$3.17971$	$[0, 1, 0, -133, 488]$	$y^2=x^3+x^2-133x+488$	2.3.0.a.1, 12.6.0.b.1, 26.6.0.b.1, 156.12.0.?	$[(4, 6)]$
3900.n1	3900k1	3900.n	3900k	$2$	$2$	$ 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 $	$ 2^{4} \cdot 3^{4} \cdot 5^{8} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.3	2B	$1560$	$48$	$0$	$1$	$1$	$1$	$2304$	$0.749562$	$8077950976/26325$	$0.94883$	$4.26203$	$[0, 1, 0, -2633, 50988]$	$y^2=x^3+x^2-2633x+50988$	2.3.0.a.1, 4.6.0.b.1, 26.6.0.b.1, 52.12.0.e.1, 120.12.0.?, $\ldots$	$[]$
3900.n2	3900k2	3900.n	3900k	$2$	$2$	$ 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 $	$ - 2^{8} \cdot 3^{2} \cdot 5^{10} \cdot 13^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.5	2B	$1560$	$48$	$0$	$1$	$1$	$1$	$4608$	$1.096136$	$-94875856/950625$	$0.90630$	$4.41150$	$[0, 1, 0, -1508, 95988]$	$y^2=x^3+x^2-1508x+95988$	2.3.0.a.1, 4.6.0.a.1, 52.12.0.d.1, 120.12.0.?, 312.24.0.?, $\ldots$	$[]$

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Elliptic curves over $\Q$
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Genus 2 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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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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