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	90a	Isogeny class
Conductor	90	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	8	Modular degree for the optimal curve
Δ	-13500 = -1 · 22 · 33 · 53	Discriminant
Eigenvalues	2+ 3+ 5-  2  6 -4 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,6,0]	[a1,a2,a3,a4,a6]
j	804357/500	j-invariant
L	0.81997845705798	L(r)(E,1)/r!
Ω	2.4599353711739	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	720g1 2880c1 90b3 450e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 90a1

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
+	+	-	2	6	-4	-6	-4	0	-6	-4	8	0	8	0	-6	6	2	-4	-12	-10	-4	12	12	2

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Quadratic twists for elliptic curve 90a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37
720g1	2880c1	90b3	450e1	4410c1	10890bi1	15210z1	26010c1	32490bf1	47610f1	75690z1	86490j1	123210cc1

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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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