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	396c	Isogeny class
Conductor	396	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	60	Modular degree for the optimal curve
Δ	-2052864 = -1 · 28 · 36 · 11	Discriminant
Eigenvalues	2- 3-  3  2 11- -4 -6  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,24,52]	[a1,a2,a3,a4,a6]
j	8192/11	j-invariant
L	1.7632679755062	L(r)(E,1)/r!
Ω	1.7632679755062	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1584o1 6336r1 44a1 9900q1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 396c1

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
-	-	3	2	-	-4	-6	8	3	0	5	-1	0	-10	0	6	-3	-4	-1	-15	-4	2	-6	9	-7

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Quadratic twists for elliptic curve 396c1

-4	8	-3	5	-7	-11	13	17
1584o1	6336r1	44a1	9900q1	19404bd1	4356h1	66924k1	114444i1

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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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