Cremona's table of elliptic curves

396 = 2² · 3² · 11

Field	Data	Notes
Atkin-Lehner	2- 3- 11+	Signs for the Atkin-Lehner involutions
Class	396b	Isogeny class
Conductor	396	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	-1154736 = -1 · 24 · 38 · 11	Discriminant
Eigenvalues	2- 3- -2 -2 11+ -2 -4 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,24,25]	[a1,a2,a3,a4,a6]
Generators	[2:9:1]	Generators of the group modulo torsion
j	131072/99	j-invariant
L	1.6410582465732	L(r)(E,1)/r!
Ω	1.7552831657878	Real period
R	0.3116416918856	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1584r1 6336ba1 132a1 9900k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 396b1

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	-2	+	-2	-4	-6	0	8	-8	10	-8	-2	8	2	-12	10	12	-8	6	-2	-16	14	-2

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Quadratic twists for elliptic curve 396b1

-4	8	-3	5	-7	-11	13	17
1584r1	6336ba1	132a1	9900k1	19404r1	4356f1	66924n1	114444p1

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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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