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 (32 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	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
23520.c1	23520a1	23520.c	23520a	$1$	$1$	$ 2^{5} \cdot 3 \cdot 5 \cdot 7^{2} $	$ - 2^{9} \cdot 3^{2} \cdot 5^{3} \cdot 7^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$2.518738087$	$1$	$2$	$12672$	$0.432908$	$-392/1125$	$1.07390$	$2.83166$	$[0, -1, 0, -16, -1784]$	$y^2=x^3-x^2-16x-1784$	40.2.0.a.1	$[(13, 6)]$
23520.x1	23520bm1	23520.x	23520bm	$1$	$1$	$ 2^{5} \cdot 3 \cdot 5 \cdot 7^{2} $	$ - 2^{9} \cdot 3^{2} \cdot 5^{3} \cdot 7^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$1$	$1$	$0$	$88704$	$1.405863$	$-392/1125$	$1.07390$	$3.99160$	$[0, -1, 0, -800, -613500]$	$y^2=x^3-x^2-800x-613500$	40.2.0.a.1	$[]$
23520.bj1	23520bo1	23520.bj	23520bo	$1$	$1$	$ 2^{5} \cdot 3 \cdot 5 \cdot 7^{2} $	$ - 2^{9} \cdot 3^{2} \cdot 5^{3} \cdot 7^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$0.421534267$	$1$	$6$	$12672$	$0.432908$	$-392/1125$	$1.07390$	$2.83166$	$[0, 1, 0, -16, 1784]$	$y^2=x^3+x^2-16x+1784$	40.2.0.a.1	$[(2, 42)]$
23520.bn1	23520z1	23520.bn	23520z	$1$	$1$	$ 2^{5} \cdot 3 \cdot 5 \cdot 7^{2} $	$ - 2^{9} \cdot 3^{2} \cdot 5^{3} \cdot 7^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$1$	$1$	$0$	$88704$	$1.405863$	$-392/1125$	$1.07390$	$3.99160$	$[0, 1, 0, -800, 613500]$	$y^2=x^3+x^2-800x+613500$	40.2.0.a.1	$[]$
47040.br1	47040t1	47040.br	47040t	$1$	$1$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7^{2} $	$ - 2^{15} \cdot 3^{2} \cdot 5^{3} \cdot 7^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$1$	$1$	$0$	$354816$	$1.752436$	$-392/1125$	$1.07390$	$4.12099$	$[0, -1, 0, -3201, 4911201]$	$y^2=x^3-x^2-3201x+4911201$	40.2.0.a.1	$[]$
47040.ca1	47040z1	47040.ca	47040z	$1$	$1$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7^{2} $	$ - 2^{15} \cdot 3^{2} \cdot 5^{3} \cdot 7^{4} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$0.135585004$	$1$	$30$	$50688$	$0.779482$	$-392/1125$	$1.07390$	$3.03579$	$[0, -1, 0, -65, 14337]$	$y^2=x^3-x^2-65x+14337$	40.2.0.a.1	$[(89, 840), (-16, 105)]$
47040.dx1	47040cr1	47040.dx	47040cr	$1$	$1$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7^{2} $	$ - 2^{15} \cdot 3^{2} \cdot 5^{3} \cdot 7^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$4.293861882$	$1$	$2$	$354816$	$1.752436$	$-392/1125$	$1.07390$	$4.12099$	$[0, 1, 0, -3201, -4911201]$	$y^2=x^3+x^2-3201x-4911201$	40.2.0.a.1	$[(227, 2472)]$
47040.hh1	47040da1	47040.hh	47040da	$1$	$1$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7^{2} $	$ - 2^{15} \cdot 3^{2} \cdot 5^{3} \cdot 7^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$0.703522500$	$1$	$4$	$50688$	$0.779482$	$-392/1125$	$1.07390$	$3.03579$	$[0, 1, 0, -65, -14337]$	$y^2=x^3+x^2-65x-14337$	40.2.0.a.1	$[(31, 120)]$
70560.b1	70560bd1	70560.b	70560bd	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 7^{2} $	$ - 2^{9} \cdot 3^{8} \cdot 5^{3} \cdot 7^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$4.310194089$	$1$	$2$	$709632$	$1.955170$	$-392/1125$	$1.07390$	$4.18924$	$[0, 0, 0, -7203, 16571702]$	$y^2=x^3-7203x+16571702$	40.2.0.a.1	$[(-251, 1602)]$
70560.cc1	70560dp1	70560.cc	70560dp	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 7^{2} $	$ - 2^{9} \cdot 3^{8} \cdot 5^{3} \cdot 7^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$1$	$1$	$0$	$709632$	$1.955170$	$-392/1125$	$1.07390$	$4.18924$	$[0, 0, 0, -7203, -16571702]$	$y^2=x^3-7203x-16571702$	40.2.0.a.1	$[]$
70560.ch1	70560bf1	70560.ch	70560bf	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 7^{2} $	$ - 2^{9} \cdot 3^{8} \cdot 5^{3} \cdot 7^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$0.463327873$	$1$	$6$	$101376$	$0.982214$	$-392/1125$	$1.07390$	$3.14344$	$[0, 0, 0, -147, -48314]$	$y^2=x^3-147x-48314$	40.2.0.a.1	$[(77, 630)]$
70560.ef1	70560dt1	70560.ef	70560dt	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 5 \cdot 7^{2} $	$ - 2^{9} \cdot 3^{8} \cdot 5^{3} \cdot 7^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$1$	$1$	$0$	$101376$	$0.982214$	$-392/1125$	$1.07390$	$3.14344$	$[0, 0, 0, -147, 48314]$	$y^2=x^3-147x+48314$	40.2.0.a.1	$[]$
117600.g1	117600fj1	117600.g	117600fj	$1$	$1$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 7^{2} $	$ - 2^{9} \cdot 3^{2} \cdot 5^{9} \cdot 7^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$4.359869511$	$1$	$2$	$2128896$	$2.210583$	$-392/1125$	$1.07390$	$4.26846$	$[0, -1, 0, -20008, 76727512]$	$y^2=x^3-x^2-20008x+76727512$	40.2.0.a.1	$[(97, 8700)]$
117600.dw1	117600h1	117600.dw	117600h	$1$	$1$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 7^{2} $	$ - 2^{9} \cdot 3^{2} \cdot 5^{9} \cdot 7^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$0.755361290$	$1$	$4$	$304128$	$1.237627$	$-392/1125$	$1.07390$	$3.26843$	$[0, -1, 0, -408, 223812]$	$y^2=x^3-x^2-408x+223812$	40.2.0.a.1	$[(72, 750)]$
117600.el1	117600gm1	117600.el	117600gm	$1$	$1$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 7^{2} $	$ - 2^{9} \cdot 3^{2} \cdot 5^{9} \cdot 7^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$1.174729950$	$1$	$2$	$304128$	$1.237627$	$-392/1125$	$1.07390$	$3.26843$	$[0, 1, 0, -408, -223812]$	$y^2=x^3+x^2-408x-223812$	40.2.0.a.1	$[(303, 5250)]$
117600.ib1	117600di1	117600.ib	117600di	$1$	$1$	$ 2^{5} \cdot 3 \cdot 5^{2} \cdot 7^{2} $	$ - 2^{9} \cdot 3^{2} \cdot 5^{9} \cdot 7^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$10.76680992$	$1$	$0$	$2128896$	$2.210583$	$-392/1125$	$1.07390$	$4.26846$	$[0, 1, 0, -20008, -76727512]$	$y^2=x^3+x^2-20008x-76727512$	40.2.0.a.1	$[(788738/11, 700277250/11)]$
141120.o1	141120nc1	141120.o	141120nc	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7^{2} $	$ - 2^{15} \cdot 3^{8} \cdot 5^{3} \cdot 7^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$1$	$1$	$0$	$405504$	$1.328787$	$-392/1125$	$1.07390$	$3.31043$	$[0, 0, 0, -588, 386512]$	$y^2=x^3-588x+386512$	40.2.0.a.1	$[]$
141120.hn1	141120nq1	141120.hn	141120nq	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7^{2} $	$ - 2^{15} \cdot 3^{8} \cdot 5^{3} \cdot 7^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$1$	$1$	$0$	$405504$	$1.328787$	$-392/1125$	$1.07390$	$3.31043$	$[0, 0, 0, -588, -386512]$	$y^2=x^3-588x-386512$	40.2.0.a.1	$[]$
141120.im1	141120id1	141120.im	141120id	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7^{2} $	$ - 2^{15} \cdot 3^{8} \cdot 5^{3} \cdot 7^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$1$	$1$	$0$	$2838528$	$2.301743$	$-392/1125$	$1.07390$	$4.29509$	$[0, 0, 0, -28812, -132573616]$	$y^2=x^3-28812x-132573616$	40.2.0.a.1	$[]$
141120.pp1	141120kh1	141120.pp	141120kh	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7^{2} $	$ - 2^{15} \cdot 3^{8} \cdot 5^{3} \cdot 7^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$1$	$1$	$0$	$2838528$	$2.301743$	$-392/1125$	$1.07390$	$4.29509$	$[0, 0, 0, -28812, 132573616]$	$y^2=x^3-28812x+132573616$	40.2.0.a.1	$[]$
235200.w1	235200w1	235200.w	235200w	$1$	$1$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{2} $	$ - 2^{15} \cdot 3^{2} \cdot 5^{9} \cdot 7^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$1$	$1$	$0$	$8515584$	$2.557156$	$-392/1125$	$1.07390$	$4.36550$	$[0, -1, 0, -80033, -613740063]$	$y^2=x^3-x^2-80033x-613740063$	40.2.0.a.1	$[]$
235200.np1	235200np1	235200.np	235200np	$1$	$1$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{2} $	$ - 2^{15} \cdot 3^{2} \cdot 5^{9} \cdot 7^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$1.457311165$	$1$	$2$	$1216512$	$1.584200$	$-392/1125$	$1.07390$	$3.42151$	$[0, -1, 0, -1633, -1788863]$	$y^2=x^3-x^2-1633x-1788863$	40.2.0.a.1	$[(187, 2100)]$
235200.pq1	235200pq1	235200.pq	235200pq	$1$	$1$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{2} $	$ - 2^{15} \cdot 3^{2} \cdot 5^{9} \cdot 7^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$1$	$1$	$0$	$1216512$	$1.584200$	$-392/1125$	$1.07390$	$3.42151$	$[0, 1, 0, -1633, 1788863]$	$y^2=x^3+x^2-1633x+1788863$	40.2.0.a.1	$[]$
235200.bbx1	235200bbx1	235200.bbx	235200bbx	$1$	$1$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{2} $	$ - 2^{15} \cdot 3^{2} \cdot 5^{9} \cdot 7^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$4.251531782$	$1$	$2$	$8515584$	$2.557156$	$-392/1125$	$1.07390$	$4.36550$	$[0, 1, 0, -80033, 613740063]$	$y^2=x^3+x^2-80033x+613740063$	40.2.0.a.1	$[(1378, 55875)]$
352800.v1	352800v1	352800.v	352800v	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ - 2^{9} \cdot 3^{8} \cdot 5^{9} \cdot 7^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$2.417827653$	$1$	$2$	$2433024$	$1.786932$	$-392/1125$	$1.07390$	$3.50336$	$[0, 0, 0, -3675, -6039250]$	$y^2=x^3-3675x-6039250$	40.2.0.a.1	$[(205, 1350)]$
352800.y1	352800y1	352800.y	352800y	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ - 2^{9} \cdot 3^{8} \cdot 5^{9} \cdot 7^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$1$	$1$	$0$	$17031168$	$2.759888$	$-392/1125$	$1.07390$	$4.41739$	$[0, 0, 0, -180075, 2071462750]$	$y^2=x^3-180075x+2071462750$	40.2.0.a.1	$[]$
352800.of1	352800of1	352800.of	352800of	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ - 2^{9} \cdot 3^{8} \cdot 5^{9} \cdot 7^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$1$	$1$	$0$	$2433024$	$1.786932$	$-392/1125$	$1.07390$	$3.50336$	$[0, 0, 0, -3675, 6039250]$	$y^2=x^3-3675x+6039250$	40.2.0.a.1	$[]$
352800.oi1	352800oi1	352800.oi	352800oi	$1$	$1$	$ 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ - 2^{9} \cdot 3^{8} \cdot 5^{9} \cdot 7^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$18.48025039$	$1$	$0$	$17031168$	$2.759888$	$-392/1125$	$1.07390$	$4.41739$	$[0, 0, 0, -180075, -2071462750]$	$y^2=x^3-180075x-2071462750$	40.2.0.a.1	$[(4952945230/673, 348035284827000/673)]$
705600.dd1	-	705600.dd	-	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ - 2^{15} \cdot 3^{8} \cdot 5^{9} \cdot 7^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$11.41784179$	$1$	$0$	$68124672$	$3.106461$	$-392/1125$	$1.07390$	$4.49885$	$[0, 0, 0, -720300, -16571702000]$	$y^2=x^3-720300x-16571702000$	40.2.0.a.1	$[(1003466/13, 953835336/13)]$
705600.dk1	-	705600.dk	-	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ - 2^{15} \cdot 3^{8} \cdot 5^{9} \cdot 7^{4} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$0.766031579$	$1$	$18$	$9732096$	$2.133507$	$-392/1125$	$1.07390$	$3.63186$	$[0, 0, 0, -14700, 48314000]$	$y^2=x^3-14700x+48314000$	40.2.0.a.1	$[(-70, 7000), (490, 12600)]$
705600.bzm1	-	705600.bzm	-	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ - 2^{15} \cdot 3^{8} \cdot 5^{9} \cdot 7^{10} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$7.983813854$	$1$	$0$	$68124672$	$3.106461$	$-392/1125$	$1.07390$	$4.49885$	$[0, 0, 0, -720300, 16571702000]$	$y^2=x^3-720300x+16571702000$	40.2.0.a.1	$[(53470/3, 12721400/3)]$
705600.bzt1	-	705600.bzt	-	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} $	$ - 2^{15} \cdot 3^{8} \cdot 5^{9} \cdot 7^{4} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$40$	$2$	$0$	$1$	$1$	$0$	$9732096$	$2.133507$	$-392/1125$	$1.07390$	$3.63186$	$[0, 0, 0, -14700, -48314000]$	$y^2=x^3-14700x-48314000$	40.2.0.a.1	$[]$

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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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