LMFDB - Elliptic curves over $\Q$ of conductor 2535

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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 (31 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
2535.a1	2535b1	2535.a	2535b	$1$	$1$	$ 3 \cdot 5 \cdot 13^{2} $	$ - 3^{7} \cdot 5 \cdot 13^{9} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$390$	$2$	$0$	$0.492375070$	$1$		$4$	$14112$	$1.475042$	$-762549907456/24024195$	$[0, -1, 1, -32166, 2290862]$	$y^2+y=x^3-x^2-32166x+2290862$	390.2.0.?
2535.b1	2535h1	2535.b	2535h	$1$	$1$	$ 3 \cdot 5 \cdot 13^{2} $	$ - 3 \cdot 5 \cdot 13^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$390$	$2$	$0$	$1$	$1$		$0$	$2016$	$0.401890$	$-4096/195$	$[0, 1, 1, -56, -1504]$	$y^2+y=x^3+x^2-56x-1504$	390.2.0.?
2535.c1	2535l1	2535.c	2535l	$1$	$1$	$ 3 \cdot 5 \cdot 13^{2} $	$ - 3^{3} \cdot 5^{2} \cdot 13^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$6$	$2$	$0$	$0.092552971$	$1$		$8$	$576$	$-0.258699$	$-18264064/675$	$[0, 1, 1, -30, 56]$	$y^2+y=x^3+x^2-30x+56$	6.2.0.a.1
2535.d1	2535k1	2535.d	2535k	$1$	$1$	$ 3 \cdot 5 \cdot 13^{2} $	$ - 3^{3} \cdot 5^{7} \cdot 13^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$390$	$2$	$0$	$0.112461220$	$1$		$10$	$14112$	$1.407328$	$-32278933504/27421875$	$[0, 1, 1, -11210, -721444]$	$y^2+y=x^3+x^2-11210x-721444$	390.2.0.?
2535.e1	2535i2	2535.e	2535i	$2$	$2$	$ 3 \cdot 5 \cdot 13^{2} $	$ 3^{6} \cdot 5^{2} \cdot 13^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$0.188699089$	$1$		$10$	$1152$	$0.511515$	$258840217117/18225$	$[1, 0, 0, -1726, 27455]$	$y^2+xy=x^3-1726x+27455$	2.3.0.a.1, 12.6.0.f.1, 26.6.0.b.1, 156.12.0.?
2535.e2	2535i1	2535.e	2535i	$2$	$2$	$ 3 \cdot 5 \cdot 13^{2} $	$ - 3^{3} \cdot 5^{4} \cdot 13^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$0.377398178$	$1$		$9$	$576$	$0.164941$	$-51895117/16875$	$[1, 0, 0, -101, 480]$	$y^2+xy=x^3-101x+480$	2.3.0.a.1, 12.6.0.f.1, 52.6.0.c.1, 78.6.0.?, 156.12.0.?
2535.f1	2535c1	2535.f	2535c	$1$	$1$	$ 3 \cdot 5 \cdot 13^{2} $	$ - 3^{3} \cdot 5^{3} \cdot 13^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.6.0.1	3Ns	$390$	$24$	$1$	$1$	$1$		$0$	$5616$	$1.285877$	$2097152/3375$	$[0, -1, 1, 5859, 228386]$	$y^2+y=x^3-x^2+5859x+228386$	3.6.0.b.1, 30.12.0.b.1, 39.12.0.a.1, 390.24.1.?
2535.g1	2535d1	2535.g	2535d	$1$	$1$	$ 3 \cdot 5 \cdot 13^{2} $	$ - 3^{3} \cdot 5^{3} \cdot 13^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.6.0.1	3Ns	$390$	$24$	$1$	$0.236654977$	$1$		$6$	$432$	$0.003403$	$2097152/3375$	$[0, -1, 1, 35, 93]$	$y^2+y=x^3-x^2+35x+93$	3.6.0.b.1, 30.12.0.b.1, 39.12.0.a.1, 390.24.1.?
2535.h1	2535e2	2535.h	2535e	$2$	$3$	$ 3 \cdot 5 \cdot 13^{2} $	$ - 3^{3} \cdot 5^{12} \cdot 13^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.2	3B.1.2	$6$	$16$	$0$	$1$	$1$		$0$	$44928$	$2.307999$	$-21752792449024/6591796875$	$[0, 1, 1, -543391, -190489685]$	$y^2+y=x^3+x^2-543391x-190489685$	3.8.0-3.a.1.1, 6.16.0-6.b.1.1
2535.h2	2535e1	2535.h	2535e	$2$	$3$	$ 3 \cdot 5 \cdot 13^{2} $	$ - 3^{9} \cdot 5^{4} \cdot 13^{8} $	$0$	$\Z/3\Z$	$\Q$	$\mathrm{SU}(2)$	$3$	3.8.0.1	3B.1.1	$6$	$16$	$0$	$1$	$1$		$2$	$14976$	$1.758692$	$16742875136/12301875$	$[0, 1, 1, 49799, 2237746]$	$y^2+y=x^3+x^2+49799x+2237746$	3.8.0-3.a.1.2, 6.16.0-6.b.1.2
2535.i1	2535j2	2535.i	2535j	$2$	$3$	$ 3 \cdot 5 \cdot 13^{2} $	$ - 3^{3} \cdot 5^{12} \cdot 13^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$78$	$16$	$0$	$0.297404560$	$1$		$6$	$3456$	$1.025522$	$-21752792449024/6591796875$	$[0, 1, 1, -3215, -87694]$	$y^2+y=x^3+x^2-3215x-87694$	3.4.0.a.1, 6.8.0.b.1, 39.8.0-3.a.1.2, 78.16.0.?
2535.i2	2535j1	2535.i	2535j	$2$	$3$	$ 3 \cdot 5 \cdot 13^{2} $	$ - 3^{9} \cdot 5^{4} \cdot 13^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.4.0.1	3B	$78$	$16$	$0$	$0.099134853$	$1$		$8$	$1152$	$0.476216$	$16742875136/12301875$	$[0, 1, 1, 295, 1109]$	$y^2+y=x^3+x^2+295x+1109$	3.4.0.a.1, 6.8.0.b.1, 39.8.0-3.a.1.1, 78.16.0.?
2535.j1	2535a7	2535.j	2535a	$8$	$16$	$ 3 \cdot 5 \cdot 13^{2} $	$ 3^{4} \cdot 5 \cdot 13^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.121	2B	$6240$	$768$	$13$	$16.45312041$	$1$		$0$	$9216$	$1.573345$	$1114544804970241/405$	$[1, 1, 0, -365043, -85043772]$	$y^2+xy=x^3+x^2-365043x-85043772$	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 10.6.0.a.1, 16.48.0.x.2, $\ldots$
2535.j2	2535a5	2535.j	2535a	$8$	$16$	$ 3 \cdot 5 \cdot 13^{2} $	$ 3^{8} \cdot 5^{2} \cdot 13^{6} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.123	2Cs	$3120$	$768$	$13$	$8.226560205$	$1$		$2$	$4608$	$1.226770$	$272223782641/164025$	$[1, 1, 0, -22818, -1335537]$	$y^2+xy=x^3+x^2-22818x-1335537$	2.6.0.a.1, 4.12.0.b.1, 8.48.0.k.1, 20.24.0.c.1, 40.96.1.cc.2, $\ldots$
2535.j3	2535a8	2535.j	2535a	$8$	$16$	$ 3 \cdot 5 \cdot 13^{2} $	$ - 3^{16} \cdot 5 \cdot 13^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.134	2B	$6240$	$768$	$13$	$16.45312041$	$1$		$0$	$9216$	$1.573345$	$-147281603041/215233605$	$[1, 1, 0, -18593, -1840002]$	$y^2+xy=x^3+x^2-18593x-1840002$	2.3.0.a.1, 4.6.0.c.1, 8.24.0.ba.2, 16.48.0.u.2, 20.12.0.h.1, $\ldots$
2535.j4	2535a4	2535.j	2535a	$8$	$16$	$ 3 \cdot 5 \cdot 13^{2} $	$ 3 \cdot 5 \cdot 13^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	32.48.0.1	2B	$6240$	$768$	$13$	$4.113280102$	$1$		$0$	$2304$	$0.880198$	$56667352321/15$	$[1, 1, 0, -13523, 599682]$	$y^2+xy=x^3+x^2-13523x+599682$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.g.1, 24.24.0.by.2, $\ldots$
2535.j5	2535a3	2535.j	2535a	$8$	$16$	$ 3 \cdot 5 \cdot 13^{2} $	$ 3^{4} \cdot 5^{4} \cdot 13^{6} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.44	2Cs	$3120$	$768$	$13$	$4.113280102$	$1$		$2$	$2304$	$0.880198$	$111284641/50625$	$[1, 1, 0, -1693, -13112]$	$y^2+xy=x^3+x^2-1693x-13112$	2.6.0.a.1, 4.24.0.b.1, 8.48.0.b.2, 24.96.1.n.1, 40.96.1.s.1, $\ldots$
2535.j6	2535a2	2535.j	2535a	$8$	$16$	$ 3 \cdot 5 \cdot 13^{2} $	$ 3^{2} \cdot 5^{2} \cdot 13^{6} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.3	2Cs	$3120$	$768$	$13$	$2.056640051$	$1$		$6$	$1152$	$0.533624$	$13997521/225$	$[1, 1, 0, -848, 9027]$	$y^2+xy=x^3+x^2-848x+9027$	2.6.0.a.1, 4.12.0.b.1, 8.24.0.i.1, 16.48.0.d.2, 24.48.0.bb.2, $\ldots$
2535.j7	2535a1	2535.j	2535a	$8$	$16$	$ 3 \cdot 5 \cdot 13^{2} $	$ - 3 \cdot 5 \cdot 13^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	32.48.0.1	2B	$6240$	$768$	$13$	$4.113280102$	$1$		$3$	$576$	$0.187050$	$-1/15$	$[1, 1, 0, -3, 408]$	$y^2+xy=x^3+x^2-3x+408$	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.g.1, 24.24.0.bz.1, $\ldots$
2535.j8	2535a6	2535.j	2535a	$8$	$16$	$ 3 \cdot 5 \cdot 13^{2} $	$ - 3^{2} \cdot 5^{8} \cdot 13^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.197	2B	$6240$	$768$	$13$	$2.056640051$	$1$		$2$	$4608$	$1.226770$	$4733169839/3515625$	$[1, 1, 0, 5912, -90683]$	$y^2+xy=x^3+x^2+5912x-90683$	2.3.0.a.1, 4.12.0.d.1, 8.48.0.n.2, 24.96.1.cv.2, 52.24.0-4.d.1.1, $\ldots$
2535.k1	2535f7	2535.k	2535f	$8$	$16$	$ 3 \cdot 5 \cdot 13^{2} $	$ 3 \cdot 5^{4} \cdot 13^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.111	2B	$6240$	$768$	$13$	$1$	$16$	$2$	$0$	$64512$	$2.471893$	$242970740812818720001/24375$	$[1, 0, 1, -21970004, -39638148769]$	$y^2+xy+y=x^3-21970004x-39638148769$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.7, 12.12.0-4.c.1.2, 16.48.0-16.g.1.9, $\ldots$
2535.k2	2535f5	2535.k	2535f	$8$	$16$	$ 3 \cdot 5 \cdot 13^{2} $	$ 3^{2} \cdot 5^{8} \cdot 13^{8} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.143	2Cs	$3120$	$768$	$13$	$1$	$16$	$2$	$2$	$32256$	$2.125317$	$59319456301170001/594140625$	$[1, 0, 1, -1373129, -619428769]$	$y^2+xy+y=x^3-1373129x-619428769$	2.6.0.a.1, 4.12.0.b.1, 8.48.0-8.i.1.1, 12.24.0-4.b.1.2, 24.96.0-24.bb.1.13, $\ldots$
2535.k3	2535f8	2535.k	2535f	$8$	$16$	$ 3 \cdot 5 \cdot 13^{2} $	$ - 3 \cdot 5^{16} \cdot 13^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.111	2B	$6240$	$768$	$13$	$1$	$16$	$2$	$0$	$64512$	$2.471893$	$-55150149867714721/5950927734375$	$[1, 0, 1, -1340174, -650564653]$	$y^2+xy+y=x^3-1340174x-650564653$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.7, 12.12.0-4.c.1.1, 16.48.0-16.g.1.9, $\ldots$
2535.k4	2535f3	2535.k	2535f	$8$	$16$	$ 3 \cdot 5 \cdot 13^{2} $	$ 3^{4} \cdot 5^{4} \cdot 13^{10} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.43	2Cs	$3120$	$768$	$13$	$1$	$4$	$2$	$2$	$16128$	$1.778744$	$15551989015681/1445900625$	$[1, 0, 1, -87884, -9194443]$	$y^2+xy+y=x^3-87884x-9194443$	2.6.0.a.1, 4.24.0.b.1, 8.48.0-4.b.1.1, 24.96.0-24.b.1.14, 40.96.0-40.b.2.23, $\ldots$
2535.k5	2535f2	2535.k	2535f	$8$	$16$	$ 3 \cdot 5 \cdot 13^{2} $	$ 3^{8} \cdot 5^{2} \cdot 13^{8} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.82	2Cs	$3120$	$768$	$13$	$1$	$1$		$2$	$8064$	$1.432171$	$168288035761/27720225$	$[1, 0, 1, -19439, 880661]$	$y^2+xy+y=x^3-19439x+880661$	2.6.0.a.1, 4.12.0.b.1, 8.48.0-8.i.1.3, 20.24.0-4.b.1.2, 40.96.0-40.bc.2.13, $\ldots$
2535.k6	2535f1	2535.k	2535f	$8$	$16$	$ 3 \cdot 5 \cdot 13^{2} $	$ 3^{4} \cdot 5 \cdot 13^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.86	2B	$6240$	$768$	$13$	$1$	$1$		$1$	$4032$	$1.085598$	$147281603041/5265$	$[1, 0, 1, -18594, 974287]$	$y^2+xy+y=x^3-18594x+974287$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.1, 16.48.0-16.g.1.1, 20.12.0-4.c.1.2, $\ldots$
2535.k7	2535f4	2535.k	2535f	$8$	$16$	$ 3 \cdot 5 \cdot 13^{2} $	$ - 3^{16} \cdot 5 \cdot 13^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.86	2B	$6240$	$768$	$13$	$1$	$1$		$0$	$16128$	$1.778744$	$1023887723039/2798036865$	$[1, 0, 1, 35486, 4967081]$	$y^2+xy+y=x^3+35486x+4967081$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.1, 16.48.0-16.g.1.1, 20.12.0-4.c.1.1, $\ldots$
2535.k8	2535f6	2535.k	2535f	$8$	$16$	$ 3 \cdot 5 \cdot 13^{2} $	$ - 3^{2} \cdot 5^{2} \cdot 13^{14} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.61	2B	$6240$	$768$	$13$	$1$	$4$	$2$	$0$	$32256$	$2.125317$	$24487529386319/183539412225$	$[1, 0, 1, 102241, -43492993]$	$y^2+xy+y=x^3+102241x-43492993$	2.3.0.a.1, 4.12.0.d.1, 8.24.0.q.1, 16.48.0-8.q.1.1, 24.48.0.be.2, $\ldots$
2535.l1	2535m2	2535.l	2535m	$2$	$2$	$ 3 \cdot 5 \cdot 13^{2} $	$ 3^{6} \cdot 5^{2} \cdot 13^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$1$		$0$	$14976$	$1.793989$	$258840217117/18225$	$[1, 0, 1, -291698, 60610331]$	$y^2+xy+y=x^3-291698x+60610331$	2.3.0.a.1, 12.6.0.f.1, 26.6.0.b.1, 156.12.0.?
2535.l2	2535m1	2535.l	2535m	$2$	$2$	$ 3 \cdot 5 \cdot 13^{2} $	$ - 3^{3} \cdot 5^{4} \cdot 13^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$156$	$12$	$0$	$1$	$1$		$1$	$7488$	$1.447416$	$-51895117/16875$	$[1, 0, 1, -17073, 1071631]$	$y^2+xy+y=x^3-17073x+1071631$	2.3.0.a.1, 12.6.0.f.1, 52.6.0.c.1, 78.6.0.?, 156.12.0.?
2535.m1	2535g1	2535.m	2535g	$1$	$1$	$ 3 \cdot 5 \cdot 13^{2} $	$ - 3^{3} \cdot 5^{2} \cdot 13^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$6$	$2$	$0$	$1$	$1$		$0$	$7488$	$1.023775$	$-18264064/675$	$[0, 1, 1, -5126, 144005]$	$y^2+y=x^3+x^2-5126x+144005$	6.2.0.a.1

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Elliptic 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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