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	6336bs	Isogeny class
Conductor	6336	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	147197952 = 212 · 33 · 113	Discriminant
Eigenvalues	2- 3+ -2  0 11-  0 -2  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-5316,149184]	[a1,a2,a3,a4,a6]
Generators	[34:88:1]	Generators of the group modulo torsion
j	150229394496/1331	j-invariant
L	3.5623961070696	L(r)(E,1)/r!
Ω	1.6499625511981	Real period
R	0.35984615776913	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	6336bl1 3168c1 6336bj1 69696eq1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 6336bs1

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 6336bs1

-4	8	-3	-11
6336bl1	3168c1	6336bj1	69696eq1

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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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