Cremona's table of elliptic curves

3630 = 2 · 3 · 5 · 11²

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 11-	Signs for the Atkin-Lehner involutions
Class	3630n	Isogeny class
Conductor	3630	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	19200	Modular degree for the optimal curve
Δ	1894153021200 = 24 · 35 · 52 · 117	Discriminant
Eigenvalues	2- 3+ 5+  0 11- -2  2 -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-168616,26579609]	[a1,a2,a3,a4,a6]
Generators	[-467:2169:1]	Generators of the group modulo torsion
j	299270638153369/1069200	j-invariant
L	4.1833102025015	L(r)(E,1)/r!
Ω	0.72931216748569	Real period
R	2.8679832786305	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	29040cu1 116160dz1 10890v1 18150y1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3630n1

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
-	+	+	0	-	-2	2	-8	4	-2	8	-2	-6	-8	-4	2	4	6	-12	-12	-2	0	-4	-6	-14

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Quadratic twists for elliptic curve 3630n1

-4	8	-3	5	-11
29040cu1	116160dz1	10890v1	18150y1	330a1

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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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