LMFDB - Elliptic curves over $\Q$ of conductor 66424

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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

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Nonmax$\ \ell$	$abc$ quality	Szpiro ratio

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Results (22 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
66424.a1	66424p1	66424.a	66424p	$1$	$1$	$ 2^{3} \cdot 19^{2} \cdot 23 $	$ - 2^{4} \cdot 19^{6} \cdot 23 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$46$	$2$	$0$	$1.399884458$	$1$		$10$	$157248$	$1.085356$	$-1149984000/23$	$0.95837$	$3.71965$	$[0, 0, 0, -19855, 1076863]$	$y^2=x^3-19855x+1076863$	46.2.0.a.1	$[(57, 361), (81, 7)]$
66424.b1	66424g1	66424.b	66424g	$2$	$2$	$ 2^{3} \cdot 19^{2} \cdot 23 $	$ 2^{4} \cdot 19^{3} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1748$	$12$	$0$	$1.166594362$	$1$		$7$	$15520$	$0.053781$	$2725888/23$	$0.75493$	$2.37974$	$[0, 1, 0, -139, 582]$	$y^2=x^3+x^2-139x+582$	2.3.0.a.1, 76.6.0.?, 92.6.0.?, 874.6.0.?, 1748.12.0.?	$[(7, 1)]$
66424.b2	66424g2	66424.b	66424g	$2$	$2$	$ 2^{3} \cdot 19^{2} \cdot 23 $	$ - 2^{8} \cdot 19^{3} \cdot 23^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1748$	$12$	$0$	$0.583297181$	$1$		$9$	$31040$	$0.400354$	$-5488/529$	$0.79271$	$2.53158$	$[0, 1, 0, -44, 1456]$	$y^2=x^3+x^2-44x+1456$	2.3.0.a.1, 38.6.0.b.1, 92.6.0.?, 1748.12.0.?	$[(6, 38)]$
66424.c1	66424m1	66424.c	66424m	$1$	$1$	$ 2^{3} \cdot 19^{2} \cdot 23 $	$ - 2^{4} \cdot 19^{8} \cdot 23^{5} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$46$	$2$	$0$	$1$	$1$		$0$	$864000$	$2.388195$	$-1167848192416000/2323519823$	$0.92943$	$4.96555$	$[0, -1, 0, -1995728, -1086374735]$	$y^2=x^3-x^2-1995728x-1086374735$	46.2.0.a.1	$[]$
66424.d1	66424j1	66424.d	66424j	$1$	$1$	$ 2^{3} \cdot 19^{2} \cdot 23 $	$ - 2^{4} \cdot 19^{8} \cdot 23^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$46$	$2$	$0$	$5.035068109$	$1$		$2$	$241920$	$1.659822$	$748596992/4392287$	$0.92345$	$3.88024$	$[0, -1, 0, 17208, 2620753]$	$y^2=x^3-x^2+17208x+2620753$	46.2.0.a.1	$[(-24, 1481)]$
66424.e1	66424n1	66424.e	66424n	$1$	$1$	$ 2^{3} \cdot 19^{2} \cdot 23 $	$ 2^{11} \cdot 19^{7} \cdot 23 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$3496$	$2$	$0$	$1$	$1$		$0$	$138240$	$1.304409$	$778034/437$	$0.76456$	$3.49932$	$[0, -1, 0, -8784, 57292]$	$y^2=x^3-x^2-8784x+57292$	3496.2.0.?	$[]$
66424.f1	66424l1	66424.f	66424l	$1$	$1$	$ 2^{3} \cdot 19^{2} \cdot 23 $	$ - 2^{8} \cdot 19^{7} \cdot 23^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$38$	$2$	$0$	$1$	$1$		$0$	$760320$	$1.880829$	$-1411839894528/10051$	$0.91610$	$4.60992$	$[0, 0, 0, -535724, -150925436]$	$y^2=x^3-535724x-150925436$	38.2.0.a.1	$[]$
66424.g1	66424a1	66424.g	66424a	$1$	$1$	$ 2^{3} \cdot 19^{2} \cdot 23 $	$ - 2^{8} \cdot 19^{3} \cdot 23^{2} $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$38$	$2$	$0$	$0.394359362$	$1$		$16$	$20480$	$0.401193$	$27648/529$	$0.79665$	$2.52827$	$[0, 0, 0, 76, 1444]$	$y^2=x^3+76x+1444$	38.2.0.a.1	$[(6, 46), (0, 38)]$
66424.h1	66424f1	66424.h	66424f	$1$	$1$	$ 2^{3} \cdot 19^{2} \cdot 23 $	$ - 2^{8} \cdot 19^{9} \cdot 23^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$38$	$2$	$0$	$1.827336418$	$1$		$2$	$389120$	$1.873411$	$27648/529$	$0.79665$	$4.11932$	$[0, 0, 0, 27436, -9904396]$	$y^2=x^3+27436x-9904396$	38.2.0.a.1	$[(361, 6859)]$
66424.i1	66424h4	66424.i	66424h	$4$	$4$	$ 2^{3} \cdot 19^{2} \cdot 23 $	$ 2^{10} \cdot 19^{10} \cdot 23 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$3496$	$48$	$0$	$7.035344462$	$1$		$1$	$472320$	$2.023010$	$24634706148/2997383$	$0.96486$	$4.37017$	$[0, 0, 0, -220571, -35433594]$	$y^2=x^3-220571x-35433594$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 76.12.0.?, 92.12.0.?, $\ldots$	$[(-2909/3, 39052/3)]$
66424.i2	66424h2	66424.i	66424h	$4$	$4$	$ 2^{3} \cdot 19^{2} \cdot 23 $	$ 2^{8} \cdot 19^{8} \cdot 23^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$1748$	$48$	$0$	$3.517672231$	$1$		$7$	$236160$	$1.676437$	$1487354832/190969$	$0.91532$	$3.99251$	$[0, 0, 0, -54511, 4321170]$	$y^2=x^3-54511x+4321170$	2.6.0.a.1, 4.12.0-2.a.1.1, 76.24.0.?, 92.24.0.?, 1748.48.0.?	$[(-243, 1794)]$
66424.i3	66424h1	66424.i	66424h	$4$	$4$	$ 2^{3} \cdot 19^{2} \cdot 23 $	$ 2^{4} \cdot 19^{7} \cdot 23 $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$3496$	$48$	$0$	$7.035344462$	$1$		$5$	$118080$	$1.329865$	$21511084032/437$	$0.87445$	$3.98341$	$[0, 0, 0, -52706, 4657261]$	$y^2=x^3-52706x+4657261$	2.3.0.a.1, 4.12.0-4.c.1.1, 152.24.0.?, 184.24.0.?, 874.6.0.?, $\ldots$	$[(1654, 66651)]$
66424.i4	66424h3	66424.i	66424h	$4$	$4$	$ 2^{3} \cdot 19^{2} \cdot 23 $	$ - 2^{10} \cdot 19^{7} \cdot 23^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$3496$	$48$	$0$	$7.035344462$	$1$		$1$	$472320$	$2.023010$	$1296970812/5316979$	$0.88161$	$4.26764$	$[0, 0, 0, 82669, 22566110]$	$y^2=x^3+82669x+22566110$	2.3.0.a.1, 4.12.0-4.c.1.2, 38.6.0.b.1, 76.24.0.?, 184.24.0.?, $\ldots$	$[(59299/3, 14454440/3)]$
66424.j1	66424k2	66424.j	66424k	$2$	$2$	$ 2^{3} \cdot 19^{2} \cdot 23 $	$ 2^{11} \cdot 19^{6} \cdot 23^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.6	2B	$184$	$12$	$0$	$1$	$9$	$3$	$1$	$157248$	$1.342672$	$2315250/529$	$0.89506$	$3.59753$	$[0, 0, 0, -12635, -425258]$	$y^2=x^3-12635x-425258$	2.3.0.a.1, 8.6.0.b.1, 92.6.0.?, 184.12.0.?	$[]$
66424.j2	66424k1	66424.j	66424k	$2$	$2$	$ 2^{3} \cdot 19^{2} \cdot 23 $	$ - 2^{10} \cdot 19^{6} \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$184$	$12$	$0$	$1$	$9$	$3$	$1$	$78624$	$0.996099$	$13500/23$	$0.90383$	$3.13165$	$[0, 0, 0, 1805, -41154]$	$y^2=x^3+1805x-41154$	2.3.0.a.1, 8.6.0.c.1, 46.6.0.a.1, 184.12.0.?	$[]$
66424.k1	66424c1	66424.k	66424c	$1$	$1$	$ 2^{3} \cdot 19^{2} \cdot 23 $	$ - 2^{8} \cdot 19^{7} \cdot 23^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$38$	$2$	$0$	$0.433822979$	$1$		$4$	$184320$	$1.388958$	$9483264/10051$	$0.74423$	$3.53724$	$[0, 0, 0, 10108, -356668]$	$y^2=x^3+10108x-356668$	38.2.0.a.1	$[(646, 16606)]$
66424.l1	66424e1	66424.l	66424e	$1$	$1$	$ 2^{3} \cdot 19^{2} \cdot 23 $	$ - 2^{4} \cdot 19^{6} \cdot 23 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$46$	$2$	$0$	$2.401525034$	$1$		$0$	$52416$	$0.644158$	$-256/23$	$0.98486$	$2.79506$	$[0, 1, 0, -120, -6391]$	$y^2=x^3+x^2-120x-6391$	46.2.0.a.1	$[(157/2, 1805/2)]$
66424.m1	66424i1	66424.m	66424i	$1$	$1$	$ 2^{3} \cdot 19^{2} \cdot 23 $	$ - 2^{4} \cdot 19^{6} \cdot 23 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$46$	$2$	$0$	$1.513793148$	$1$		$2$	$52416$	$0.732100$	$-562432/23$	$0.75822$	$3.03927$	$[0, 1, 0, -1564, -25163]$	$y^2=x^3+x^2-1564x-25163$	46.2.0.a.1	$[(63, 361)]$
66424.n1	66424d1	66424.n	66424d	$1$	$1$	$ 2^{3} \cdot 19^{2} \cdot 23 $	$ 2^{11} \cdot 19^{13} \cdot 23 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$3496$	$2$	$0$	$35.37979269$	$1$		$0$	$3225600$	$2.939976$	$4772777079094274/20559049997$	$0.94738$	$5.52900$	$[0, 1, 0, -16080504, 24721856624]$	$y^2=x^3+x^2-16080504x+24721856624$	3496.2.0.?	$[(16770324359717155/4080261, 6637332371624003019729862/4080261)]$
66424.o1	66424b1	66424.o	66424b	$2$	$2$	$ 2^{3} \cdot 19^{2} \cdot 23 $	$ 2^{4} \cdot 19^{9} \cdot 23 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1748$	$12$	$0$	$1$	$1$		$1$	$294880$	$1.526001$	$2725888/23$	$0.75493$	$3.97078$	$[0, -1, 0, -50299, -4293480]$	$y^2=x^3-x^2-50299x-4293480$	2.3.0.a.1, 76.6.0.?, 92.6.0.?, 874.6.0.?, 1748.12.0.?	$[]$
66424.o2	66424b2	66424.o	66424b	$2$	$2$	$ 2^{3} \cdot 19^{2} \cdot 23 $	$ - 2^{8} \cdot 19^{9} \cdot 23^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$1748$	$12$	$0$	$1$	$1$		$1$	$589760$	$1.872574$	$-5488/529$	$0.79271$	$4.12262$	$[0, -1, 0, -16004, -10082476]$	$y^2=x^3-x^2-16004x-10082476$	2.3.0.a.1, 38.6.0.b.1, 92.6.0.?, 1748.12.0.?	$[]$
66424.p1	66424o1	66424.p	66424o	$1$	$1$	$ 2^{3} \cdot 19^{2} \cdot 23 $	$ - 2^{4} \cdot 19^{8} \cdot 23 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$46$	$2$	$0$	$1$	$1$		$0$	$241920$	$1.136475$	$864000/8303$	$0.73283$	$3.31924$	$[0, 0, 0, 1805, 116603]$	$y^2=x^3+1805x+116603$	46.2.0.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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