Cremona's table of elliptic curves

6336 = 2⁶ · 3² · 11

Field	Data	Notes
Atkin-Lehner	2- 3+ 11+	Signs for the Atkin-Lehner involutions
Class	6336bj	Isogeny class
Conductor	6336	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	9216	Modular degree for the optimal curve
Δ	107307307008 = 212 · 39 · 113	Discriminant
Eigenvalues	2- 3+  2  0 11+  0  2  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-47844,-4027968]	[a1,a2,a3,a4,a6]
j	150229394496/1331	j-invariant
L	2.5824558298354	L(r)(E,1)/r!
Ω	0.32280697872942	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6336bq1 3168s1 6336bs1 69696em1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 6336bj1

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	0	+	0	2	6	6	-2	0	2	-2	6	6	-2	0	-8	12	-6	6	-12	12	-8	6

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Quadratic twists for elliptic curve 6336bj1

-4	8	-3	-11
6336bq1	3168s1	6336bs1	69696em1

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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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