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	90b	Isogeny class
Conductor	90	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-9841500 = -1 · 22 · 39 · 53	Discriminant
Eigenvalues	2- 3+ 5+  2 -6 -4  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,52,-53]	[a1,a2,a3,a4,a6]
j	804357/500	j-invariant
L	1.3236980861804	L(r)(E,1)/r!
Ω	1.3236980861804	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	720f3 2880g3 90a1 450f3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 90b3

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 90b3

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37
720f3	2880g3	90a1	450f3	4410z3	10890c3	15210d3	26010bd3	32490b3	47610bm3	75690a3	86490bx3	123210m3

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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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