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	396a	Isogeny class
Conductor	396	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	240	Modular degree for the optimal curve
Δ	-7576222896 = -1 · 24 · 316 · 11	Discriminant
Eigenvalues	2- 3- -2  2 11-  6  4 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-696,-8215]	[a1,a2,a3,a4,a6]
j	-3196715008/649539	j-invariant
L	1.3791686201073	L(r)(E,1)/r!
Ω	0.4597228733691	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	1584m1 6336m1 132b1 9900r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 396a1

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

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Quadratic twists for elliptic curve 396a1

-4	8	-3	5	-7	-11	13	17
1584m1	6336m1	132b1	9900r1	19404z1	4356g1	66924j1	114444b1

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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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