LMFDB - Elliptic curves over $\Q$ of conductor 975

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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 (21 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
975.a1	975d1	975.a	975d	$1$	$1$	$ 3 \cdot 5^{2} \cdot 13 $	$ - 3^{3} \cdot 5^{13} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$390$	$2$	$0$	$1$	$1$	$0$	$2016$	$0.929571$	$-32278933504/27421875$	$0.96372$	$5.05020$	$[0, -1, 1, -1658, -40282]$	$y^2+y=x^3-x^2-1658x-40282$	390.2.0.?	$[]$
975.b1	975b1	975.b	975b	$1$	$1$	$ 3 \cdot 5^{2} \cdot 13 $	$ - 3 \cdot 5^{7} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$390$	$2$	$0$	$0.269492501$	$1$	$6$	$288$	$-0.075866$	$-4096/195$	$0.83662$	$3.25414$	$[0, -1, 1, -8, -82]$	$y^2+y=x^3-x^2-8x-82$	390.2.0.?	$[(7, 12)]$
975.c1	975i1	975.c	975i	$1$	$1$	$ 3 \cdot 5^{2} \cdot 13 $	$ - 3^{7} \cdot 5^{7} \cdot 13^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$390$	$2$	$0$	$0.018473682$	$1$	$20$	$2016$	$0.997287$	$-762549907456/24024195$	$0.97132$	$5.38611$	$[0, 1, 1, -4758, 128144]$	$y^2+y=x^3+x^2-4758x+128144$	390.2.0.?	$[(273, 4387)]$
975.d1	975e1	975.d	975e	$1$	$1$	$ 3 \cdot 5^{2} \cdot 13 $	$ - 3^{2} \cdot 5^{8} \cdot 13^{3} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$52$	$2$	$0$	$1$	$1$	$0$	$720$	$0.660023$	$-417267265/19773$	$0.90540$	$4.76625$	$[1, 1, 1, -1138, -15844]$	$y^2+xy+y=x^3+x^2-1138x-15844$	52.2.0.a.1	$[]$
975.e1	975k1	975.e	975k	$1$	$1$	$ 3 \cdot 5^{2} \cdot 13 $	$ - 3^{6} \cdot 5^{4} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$52$	$2$	$0$	$0.057170537$	$1$	$12$	$144$	$-0.020457$	$304175/9477$	$0.95479$	$3.34625$	$[1, 0, 0, 12, 117]$	$y^2+xy=x^3+12x+117$	52.2.0.a.1	$[(-3, 9)]$
975.f1	975g3	975.f	975g	$4$	$4$	$ 3 \cdot 5^{2} \cdot 13 $	$ 3^{4} \cdot 5^{6} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1560$	$48$	$0$	$1$	$1$	$0$	$512$	$0.486352$	$37159393753/1053$	$1.11616$	$4.93940$	$[1, 0, 0, -1738, -28033]$	$y^2+xy=x^3-1738x-28033$	2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.1, 24.12.0.ba.1, 26.6.0.b.1, $\ldots$	$[]$
975.f2	975g4	975.f	975g	$4$	$4$	$ 3 \cdot 5^{2} \cdot 13 $	$ 3 \cdot 5^{6} \cdot 13^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1560$	$48$	$0$	$1$	$1$	$0$	$512$	$0.486352$	$822656953/85683$	$0.96086$	$4.38575$	$[1, 0, 0, -488, 3717]$	$y^2+xy=x^3-488x+3717$	2.3.0.a.1, 4.6.0.c.1, 12.12.0.h.1, 20.12.0-4.c.1.2, 60.24.0-12.h.1.2, $\ldots$	$[]$
975.f3	975g2	975.f	975g	$4$	$4$	$ 3 \cdot 5^{2} \cdot 13 $	$ 3^{2} \cdot 5^{6} \cdot 13^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$780$	$48$	$0$	$1$	$1$	$2$	$256$	$0.139779$	$10218313/1521$	$0.91403$	$3.74814$	$[1, 0, 0, -113, -408]$	$y^2+xy=x^3-113x-408$	2.6.0.a.1, 12.12.0.a.1, 20.12.0-2.a.1.1, 52.12.0.b.1, 60.24.0-12.a.1.1, $\ldots$	$[]$
975.f4	975g1	975.f	975g	$4$	$4$	$ 3 \cdot 5^{2} \cdot 13 $	$ - 3 \cdot 5^{6} \cdot 13 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.6.0.1	2B	$1560$	$48$	$0$	$1$	$1$	$1$	$128$	$-0.206795$	$12167/39$	$0.85844$	$2.98961$	$[1, 0, 0, 12, -33]$	$y^2+xy=x^3+12x-33$	2.3.0.a.1, 4.6.0.c.1, 24.12.0.ba.1, 40.12.0-4.c.1.5, 60.12.0-4.c.1.2, $\ldots$	$[]$
975.g1	975f1	975.g	975f	$1$	$1$	$ 3 \cdot 5^{2} \cdot 13 $	$ - 3^{5} \cdot 5^{9} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$390$	$2$	$0$	$0.853487407$	$1$	$4$	$400$	$0.558144$	$-32768/3159$	$1.04783$	$4.35945$	$[0, -1, 1, -83, 3818]$	$y^2+y=x^3-x^2-83x+3818$	390.2.0.?	$[(-8, 62)]$
975.h1	975j1	975.h	975j	$1$	$1$	$ 3 \cdot 5^{2} \cdot 13 $	$ - 3^{5} \cdot 5^{3} \cdot 13 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$390$	$2$	$0$	$0.096937012$	$1$	$8$	$80$	$-0.246575$	$-32768/3159$	$1.04783$	$2.95637$	$[0, 1, 1, -3, 29]$	$y^2+y=x^3+x^2-3x+29$	390.2.0.?	$[(3, 7)]$
975.i1	975a7	975.i	975a	$8$	$16$	$ 3 \cdot 5^{2} \cdot 13 $	$ 3 \cdot 5^{10} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	32.48.0.10	2B	$6240$	$768$	$13$	$23.12562658$	$1$	$0$	$9216$	$1.994137$	$242970740812818720001/24375$	$1.04119$	$8.22326$	$[1, 1, 0, -3250000, -2256492875]$	$y^2+xy=x^3+x^2-3250000x-2256492875$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.g.1, 20.12.0-4.c.1.1, $\ldots$	$[(47745136965/2684, 9934123193216195/2684)]$
975.i2	975a5	975.i	975a	$8$	$16$	$ 3 \cdot 5^{2} \cdot 13 $	$ 3^{2} \cdot 5^{14} \cdot 13^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.7	2Cs	$3120$	$768$	$13$	$11.56281329$	$1$	$2$	$4608$	$1.647562$	$59319456301170001/594140625$	$1.01234$	$7.01472$	$[1, 1, 0, -203125, -35321000]$	$y^2+xy=x^3+x^2-203125x-35321000$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.i.1, 16.48.0-8.i.1.1, 20.24.0-4.b.1.1, $\ldots$	$[(-878361/58, 27647851/58)]$
975.i3	975a8	975.i	975a	$8$	$16$	$ 3 \cdot 5^{2} \cdot 13 $	$ - 3 \cdot 5^{22} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	32.48.0.10	2B	$6240$	$768$	$13$	$23.12562658$	$1$	$0$	$9216$	$1.994137$	$-55150149867714721/5950927734375$	$1.01425$	$7.02897$	$[1, 1, 0, -198250, -37090625]$	$y^2+xy=x^3+x^2-198250x-37090625$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.g.1, 20.12.0-4.c.1.1, $\ldots$	$[(7765202319/3538, 380236785822631/3538)]$
975.i4	975a3	975.i	975a	$8$	$16$	$ 3 \cdot 5^{2} \cdot 13 $	$ 3^{4} \cdot 5^{10} \cdot 13^{4} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.47	2Cs	$3120$	$768$	$13$	$5.781406645$	$1$	$2$	$2304$	$1.300989$	$15551989015681/1445900625$	$0.97384$	$5.81652$	$[1, 1, 0, -13000, -528125]$	$y^2+xy=x^3+x^2-13000x-528125$	2.6.0.a.1, 4.24.0.b.1, 8.48.0-4.b.1.3, 20.48.0-4.b.1.1, 24.96.0-24.b.1.8, $\ldots$	$[(-321/2, 959/2)]$
975.i5	975a2	975.i	975a	$8$	$16$	$ 3 \cdot 5^{2} \cdot 13 $	$ 3^{8} \cdot 5^{8} \cdot 13^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.74	2Cs	$3120$	$768$	$13$	$2.890703322$	$1$	$6$	$1152$	$0.954415$	$168288035761/27720225$	$1.01793$	$5.15887$	$[1, 1, 0, -2875, 49000]$	$y^2+xy=x^3+x^2-2875x+49000$	2.6.0.a.1, 4.12.0.b.1, 8.48.0-8.i.1.6, 20.24.0-4.b.1.3, 40.96.0-40.bc.2.4, $\ldots$	$[(-60, 130)]$
975.i6	975a1	975.i	975a	$8$	$16$	$ 3 \cdot 5^{2} \cdot 13 $	$ 3^{4} \cdot 5^{7} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.87	2B	$6240$	$768$	$13$	$1.445351661$	$1$	$5$	$576$	$0.607841$	$147281603041/5265$	$0.93867$	$5.13949$	$[1, 1, 0, -2750, 54375]$	$y^2+xy=x^3+x^2-2750x+54375$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.1, 16.48.0-16.g.1.16, 20.12.0-4.c.1.2, $\ldots$	$[(26, 23)]$
975.i7	975a4	975.i	975a	$8$	$16$	$ 3 \cdot 5^{2} \cdot 13 $	$ - 3^{16} \cdot 5^{7} \cdot 13 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.158	2B	$6240$	$768$	$13$	$5.781406645$	$1$	$0$	$2304$	$1.300989$	$1023887723039/2798036865$	$1.05353$	$5.61219$	$[1, 1, 0, 5250, 284625]$	$y^2+xy=x^3+x^2+5250x+284625$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.5, 16.48.0-16.g.1.12, 20.12.0-4.c.1.2, $\ldots$	$[(-635/4, 9295/4)]$
975.i8	975a6	975.i	975a	$8$	$16$	$ 3 \cdot 5^{2} \cdot 13 $	$ - 3^{2} \cdot 5^{8} \cdot 13^{8} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.198	2B	$6240$	$768$	$13$	$2.890703322$	$1$	$2$	$4608$	$1.647562$	$24487529386319/183539412225$	$1.01498$	$6.24295$	$[1, 1, 0, 15125, -2468750]$	$y^2+xy=x^3+x^2+15125x-2468750$	2.3.0.a.1, 4.12.0.d.1, 8.48.0-8.q.1.1, 20.24.0-4.d.1.1, 24.96.0-24.be.2.7, $\ldots$	$[(250, 4000)]$
975.j1	975c1	975.j	975c	$1$	$1$	$ 3 \cdot 5^{2} \cdot 13 $	$ - 3^{6} \cdot 5^{10} \cdot 13 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$52$	$2$	$0$	$1$	$1$	$0$	$720$	$0.784262$	$304175/9477$	$0.95479$	$4.74933$	$[1, 1, 0, 300, 14625]$	$y^2+xy=x^3+x^2+300x+14625$	52.2.0.a.1	$[]$
975.k1	975h1	975.k	975h	$1$	$1$	$ 3 \cdot 5^{2} \cdot 13 $	$ - 3^{2} \cdot 5^{2} \cdot 13^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$52$	$2$	$0$	$0.574557957$	$1$	$4$	$144$	$-0.144697$	$-417267265/19773$	$0.90540$	$3.36317$	$[1, 0, 1, -46, -127]$	$y^2+xy+y=x^3-46x-127$	52.2.0.a.1	$[(13, 32)]$

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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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