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	6336bp	Isogeny class
Conductor	6336	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	150730702848 = 222 · 33 · 113	Discriminant
Eigenvalues	2- 3+  0 -2 11- -2  6  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-5580,-159344]	[a1,a2,a3,a4,a6]
Generators	[-43:33:1]	Generators of the group modulo torsion
j	2714704875/21296	j-invariant
L	3.854641913944	L(r)(E,1)/r!
Ω	0.55264525025751	Real period
R	1.1624822952723	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	6336b1 1584h1 6336bi3 69696ef1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 6336bp1

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

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Quadratic twists for elliptic curve 6336bp1

-4	8	-3	-11
6336b1	1584h1	6336bi3	69696ef1

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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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