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	6336bf	Isogeny class
Conductor	6336	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	98537472 = 212 · 37 · 11	Discriminant
Eigenvalues	2+ 3- -4  2 11- -4 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-372,-2720]	[a1,a2,a3,a4,a6]
Generators	[-12:4:1]	Generators of the group modulo torsion
j	1906624/33	j-invariant
L	3.2108366751441	L(r)(E,1)/r!
Ω	1.088227890007	Real period
R	1.4752593205103	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	6336v1 3168k1 2112o1 69696dr1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 6336bf1

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
+	-	-4	2	-	-4	-2	4	6	-6	-4	2	-6	8	10	-12	0	-8	4	6	10	6	12	14	-18

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Quadratic twists for elliptic curve 6336bf1

-4	8	-3	-11
6336v1	3168k1	2112o1	69696dr1

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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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