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	Manin constant

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Results (24 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
6975.h1	6975d1	6975.h	6975d	$1$	$1$	$ 3^{2} \cdot 5^{2} \cdot 31 $	$ 3^{3} \cdot 5^{8} \cdot 31^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.30.0.2	5Ns.2.1	$930$	$120$	$5$	$1$	$1$		$0$	$24000$	$1.608330$	$3792752640000/28629151$	$1.10707$	$5.10000$	$[0, 0, 1, -71250, -7272344]$	$y^2+y=x^3-71250x-7272344$	5.30.0.b.1, 15.60.0.b.1, 186.2.0.?, 310.60.2.?, 930.120.5.?	$[ ]$
6975.i1	6975b1	6975.i	6975b	$1$	$1$	$ 3^{2} \cdot 5^{2} \cdot 31 $	$ 3^{3} \cdot 5^{2} \cdot 31^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.30.0.2	5Ns.2.1	$930$	$120$	$5$	$2.416947147$	$1$		$2$	$4800$	$0.803612$	$3792752640000/28629151$	$1.10707$	$4.00887$	$[0, 0, 1, -2850, -58179]$	$y^2+y=x^3-2850x-58179$	5.30.0.b.1, 15.60.0.b.1, 186.2.0.?, 310.60.2.?, 930.120.5.?	$[(-31, 19)]$
6975.m1	6975a1	6975.m	6975a	$1$	$1$	$ 3^{2} \cdot 5^{2} \cdot 31 $	$ 3^{9} \cdot 5^{2} \cdot 31^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.30.0.2	5Ns.2.1	$930$	$120$	$5$	$2.462027010$	$1$		$2$	$14400$	$1.352917$	$3792752640000/28629151$	$1.10707$	$4.75368$	$[0, 0, 1, -25650, 1570826]$	$y^2+y=x^3-25650x+1570826$	5.30.0.b.1, 15.60.0.b.1, 186.2.0.?, 310.60.2.?, 930.120.5.?	$[(84, 94)]$
6975.n1	6975c1	6975.n	6975c	$1$	$1$	$ 3^{2} \cdot 5^{2} \cdot 31 $	$ 3^{9} \cdot 5^{8} \cdot 31^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.30.0.2	5Ns.2.1	$930$	$120$	$5$	$1$	$1$		$0$	$72000$	$2.157635$	$3792752640000/28629151$	$1.10707$	$5.84482$	$[0, 0, 1, -641250, 196353281]$	$y^2+y=x^3-641250x+196353281$	5.30.0.b.1, 15.60.0.b.1, 186.2.0.?, 310.60.2.?, 930.120.5.?	$[ ]$
111600.db1	111600cw1	111600.db	111600cw	$1$	$1$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ 2^{12} \cdot 3^{9} \cdot 5^{2} \cdot 31^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.30.0.2	5Ns.2.1	$930$	$120$	$5$	$2.910827910$	$1$		$0$	$1036800$	$2.046066$	$3792752640000/28629151$	$1.10707$	$4.33534$	$[0, 0, 0, -410400, -100532880]$	$y^2=x^3-410400x-100532880$	5.30.0.b.1, 15.60.0.b.1, 186.2.0.?, 310.60.2.?, 930.120.5.?	$[(-9831/5, 25947/5)]$
111600.dc1	111600dk1	111600.dc	111600dk	$1$	$1$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ 2^{12} \cdot 3^{9} \cdot 5^{8} \cdot 31^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.30.0.2	5Ns.2.1	$930$	$120$	$5$	$1$	$1$		$0$	$5184000$	$2.850784$	$3792752640000/28629151$	$1.10707$	$5.16618$	$[0, 0, 0, -10260000, -12566610000]$	$y^2=x^3-10260000x-12566610000$	5.30.0.b.1, 15.60.0.b.1, 186.2.0.?, 310.60.2.?, 930.120.5.?	$[ ]$
111600.ep1	111600dj1	111600.ep	111600dj	$1$	$1$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ 2^{12} \cdot 3^{3} \cdot 5^{8} \cdot 31^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.30.0.2	5Ns.2.1	$930$	$120$	$5$	$1$	$1$		$0$	$1728000$	$2.301479$	$3792752640000/28629151$	$1.10707$	$4.59905$	$[0, 0, 0, -1140000, 465430000]$	$y^2=x^3-1140000x+465430000$	5.30.0.b.1, 15.60.0.b.1, 186.2.0.?, 310.60.2.?, 930.120.5.?	$[ ]$
111600.eq1	111600cv1	111600.eq	111600cv	$1$	$1$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ 2^{12} \cdot 3^{3} \cdot 5^{2} \cdot 31^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.30.0.2	5Ns.2.1	$930$	$120$	$5$	$1.262519626$	$1$		$0$	$345600$	$1.496759$	$3792752640000/28629151$	$1.10707$	$3.76820$	$[0, 0, 0, -45600, 3723440]$	$y^2=x^3-45600x+3723440$	5.30.0.b.1, 15.60.0.b.1, 186.2.0.?, 310.60.2.?, 930.120.5.?	$[(409/2, 2883/2)]$
216225.bb1	216225bm1	216225.bb	216225bm	$1$	$1$	$ 3^{2} \cdot 5^{2} \cdot 31^{2} $	$ 3^{9} \cdot 5^{8} \cdot 31^{11} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.30.0.2	5Ns.2.1	$930$	$120$	$5$	$3.853495904$	$1$		$0$	$69120000$	$3.874630$	$3792752640000/28629151$	$1.10707$	$5.88820$	$[0, 0, 1, -616241250, -5849560601719]$	$y^2+y=x^3-616241250x-5849560601719$	5.30.0.b.1, 15.60.0.b.1, 186.2.0.?, 310.60.2.?, 930.120.5.?	$[(-7377225/23, 2181812279/23)]$
216225.bc1	216225bq1	216225.bc	216225bq	$1$	$1$	$ 3^{2} \cdot 5^{2} \cdot 31^{2} $	$ 3^{9} \cdot 5^{2} \cdot 31^{11} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.30.0.2	5Ns.2.1	$930$	$120$	$5$	$1$	$1$		$0$	$13824000$	$3.069912$	$3792752640000/28629151$	$1.10707$	$5.10209$	$[0, 0, 1, -24649650, -46796484814]$	$y^2+y=x^3-24649650x-46796484814$	5.30.0.b.1, 15.60.0.b.1, 186.2.0.?, 310.60.2.?, 930.120.5.?	$[ ]$
216225.bi1	216225br1	216225.bi	216225br	$1$	$1$	$ 3^{2} \cdot 5^{2} \cdot 31^{2} $	$ 3^{3} \cdot 5^{2} \cdot 31^{11} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.30.0.2	5Ns.2.1	$930$	$120$	$5$	$1$	$1$		$0$	$4608000$	$2.520607$	$3792752640000/28629151$	$1.10707$	$4.56548$	$[0, 0, 1, -2738850, 1733203141]$	$y^2+y=x^3-2738850x+1733203141$	5.30.0.b.1, 15.60.0.b.1, 186.2.0.?, 310.60.2.?, 930.120.5.?	$[ ]$
216225.bj1	216225bn1	216225.bj	216225bn	$1$	$1$	$ 3^{2} \cdot 5^{2} \cdot 31^{2} $	$ 3^{3} \cdot 5^{8} \cdot 31^{11} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.30.0.2	5Ns.2.1	$930$	$120$	$5$	$9.695394227$	$1$		$0$	$23040000$	$3.325325$	$3792752640000/28629151$	$1.10707$	$5.35159$	$[0, 0, 1, -68471250, 216650392656]$	$y^2+y=x^3-68471250x+216650392656$	5.30.0.b.1, 15.60.0.b.1, 186.2.0.?, 310.60.2.?, 930.120.5.?	$[(49168046/121, 277749440251/121)]$
341775.cc1	341775cc1	341775.cc	341775cc	$1$	$1$	$ 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 31 $	$ 3^{3} \cdot 5^{2} \cdot 7^{6} \cdot 31^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.30.0.2	5Ns.2.1	$930$	$120$	$5$	$0.226116749$	$1$		$6$	$1843200$	$1.776567$	$3792752640000/28629151$	$1.10707$	$3.70072$	$[0, 0, 1, -139650, 19955311]$	$y^2+y=x^3-139650x+19955311$	5.30.0.b.1, 15.60.0.b.1, 186.2.0.?, 310.60.2.?, 930.120.5.?	$[(301, 2278)]$
341775.ce1	341775ce1	341775.ce	341775ce	$1$	$1$	$ 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 31 $	$ 3^{3} \cdot 5^{8} \cdot 7^{6} \cdot 31^{5} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.30.0.2	5Ns.2.1	$930$	$120$	$5$	$0.492518231$	$1$		$12$	$9216000$	$2.581287$	$3792752640000/28629151$	$1.10707$	$4.45859$	$[0, 0, 1, -3491250, 2494413906]$	$y^2+y=x^3-3491250x+2494413906$	5.30.0.b.1, 15.60.0.b.1, 186.2.0.?, 310.60.2.?, 930.120.5.?	$[(-1750, 56962), (2156, 70633)]$
341775.dk1	341775dk1	341775.dk	341775dk	$1$	$1$	$ 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 31 $	$ 3^{9} \cdot 5^{8} \cdot 7^{6} \cdot 31^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.30.0.2	5Ns.2.1	$930$	$120$	$5$	$1$	$1$		$0$	$27648000$	$3.130592$	$3792752640000/28629151$	$1.10707$	$4.97591$	$[0, 0, 1, -31421250, -67349175469]$	$y^2+y=x^3-31421250x-67349175469$	5.30.0.b.1, 15.60.0.b.1, 186.2.0.?, 310.60.2.?, 930.120.5.?	$[ ]$
341775.dl1	341775dl1	341775.dl	341775dl	$1$	$1$	$ 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 31 $	$ 3^{9} \cdot 5^{2} \cdot 7^{6} \cdot 31^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.30.0.2	5Ns.2.1	$930$	$120$	$5$	$1.326620397$	$1$		$4$	$5529600$	$2.325874$	$3792752640000/28629151$	$1.10707$	$4.21805$	$[0, 0, 1, -1256850, -538793404]$	$y^2+y=x^3-1256850x-538793404$	5.30.0.b.1, 15.60.0.b.1, 186.2.0.?, 310.60.2.?, 930.120.5.?	$[(-686, 759)]$
446400.hr1	446400hr1	446400.hr	446400hr	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ 2^{6} \cdot 3^{3} \cdot 5^{8} \cdot 31^{5} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.30.0.2	5Ns.2.1	$930$	$120$	$5$	$1.330048696$	$1$		$6$	$3456000$	$1.954905$	$3792752640000/28629151$	$1.10707$	$3.78926$	$[0, 0, 0, -285000, 58178750]$	$y^2=x^3-285000x+58178750$	5.30.0.b.1, 15.60.0.b.1, 186.2.0.?, 310.60.2.?, 930.120.5.?	$[(275, 775), (3625/4, 146475/4)]$
446400.hs1	446400hs1	446400.hs	446400hs	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ 2^{6} \cdot 3^{9} \cdot 5^{2} \cdot 31^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.30.0.2	5Ns.2.1	$930$	$120$	$5$	$4.972421518$	$1$		$2$	$2073600$	$1.699492$	$3792752640000/28629151$	$1.10707$	$3.55365$	$[0, 0, 0, -102600, 12566610]$	$y^2=x^3-102600x+12566610$	5.30.0.b.1, 15.60.0.b.1, 186.2.0.?, 310.60.2.?, 930.120.5.?	$[(151, 719)]$
446400.ht1	446400ht1	446400.ht	446400ht	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ 2^{6} \cdot 3^{3} \cdot 5^{2} \cdot 31^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.30.0.2	5Ns.2.1	$930$	$120$	$5$	$0.875745079$	$1$		$2$	$691200$	$1.150185$	$3792752640000/28629151$	$1.10707$	$3.04695$	$[0, 0, 0, -11400, 465430]$	$y^2=x^3-11400x+465430$	5.30.0.b.1, 15.60.0.b.1, 186.2.0.?, 310.60.2.?, 930.120.5.?	$[(-69, 961)]$
446400.hu1	446400hu1	446400.hu	446400hu	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ 2^{6} \cdot 3^{9} \cdot 5^{8} \cdot 31^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.30.0.2	5Ns.2.1	$930$	$120$	$5$	$1$	$4$	$2$	$0$	$10368000$	$2.504211$	$3792752640000/28629151$	$1.10707$	$4.29596$	$[0, 0, 0, -2565000, 1570826250]$	$y^2=x^3-2565000x+1570826250$	5.30.0.b.1, 15.60.0.b.1, 186.2.0.?, 310.60.2.?, 930.120.5.?	$[ ]$
446400.lz1	446400lz1	446400.lz	446400lz	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ 2^{6} \cdot 3^{9} \cdot 5^{2} \cdot 31^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.30.0.2	5Ns.2.1	$930$	$120$	$5$	$3.617582513$	$1$		$2$	$2073600$	$1.699492$	$3792752640000/28629151$	$1.10707$	$3.55365$	$[0, 0, 0, -102600, -12566610]$	$y^2=x^3-102600x-12566610$	5.30.0.b.1, 15.60.0.b.1, 186.2.0.?, 310.60.2.?, 930.120.5.?	$[(11739, 1271403)]$
446400.ma1	446400ma1	446400.ma	446400ma	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ 2^{6} \cdot 3^{3} \cdot 5^{8} \cdot 31^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.30.0.2	5Ns.2.1	$930$	$120$	$5$	$1$	$1$		$0$	$3456000$	$1.954905$	$3792752640000/28629151$	$1.10707$	$3.78926$	$[0, 0, 0, -285000, -58178750]$	$y^2=x^3-285000x-58178750$	5.30.0.b.1, 15.60.0.b.1, 186.2.0.?, 310.60.2.?, 930.120.5.?	$[ ]$
446400.mb1	446400mb1	446400.mb	446400mb	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ 2^{6} \cdot 3^{9} \cdot 5^{8} \cdot 31^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.30.0.2	5Ns.2.1	$930$	$120$	$5$	$1$	$1$		$0$	$10368000$	$2.504211$	$3792752640000/28629151$	$1.10707$	$4.29596$	$[0, 0, 0, -2565000, -1570826250]$	$y^2=x^3-2565000x-1570826250$	5.30.0.b.1, 15.60.0.b.1, 186.2.0.?, 310.60.2.?, 930.120.5.?	$[ ]$
446400.mc1	446400mc1	446400.mc	446400mc	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 31 $	$ 2^{6} \cdot 3^{3} \cdot 5^{2} \cdot 31^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.30.0.2	5Ns.2.1	$930$	$120$	$5$	$11.88046221$	$1$		$0$	$691200$	$1.150185$	$3792752640000/28629151$	$1.10707$	$3.04695$	$[0, 0, 0, -11400, -465430]$	$y^2=x^3-11400x-465430$	5.30.0.b.1, 15.60.0.b.1, 186.2.0.?, 310.60.2.?, 930.120.5.?	$[(227911/19, 107135349/19)]$

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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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