Cremona's table of elliptic curves

90 = 2 · 3² · 5

Field	Data	Notes
Atkin-Lehner	2- 3- 5-	Signs for the Atkin-Lehner involutions
Class	90c	Isogeny class
Conductor	90	Conductor
∏ cp	144	Product of Tamagawa factors cp
Δ	-1119744000 = -1 · 212 · 37 · 53	Discriminant
Eigenvalues	2- 3- 5- -4  0  2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-122,1721]	[a1,a2,a3,a4,a6]
j	-273359449/1536000	j-invariant
L	1.3375959945886	L(r)(E,1)/r!
Ω	1.3375959945886	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	12	Number of elements in the torsion subgroup
Twists	720j3 2880n3 30a3 450g3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 90c3

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	-	-	-4	0	2	-6	-4	0	6	8	2	6	-4	0	6	0	-10	-4	0	2	8	-12	-18	2

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Quadratic twists for elliptic curve 90c3

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37
720j3	2880n3	30a3	450g3	4410bb3	10890ba3	15210n3	26010bm3	32490ba3	47610bz3	75690t3	86490cx3	123210bi3

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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