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	6336bg	Isogeny class
Conductor	6336	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-43693350246678528 = -1 · 223 · 316 · 112	Discriminant
Eigenvalues	2+ 3- -4 -2 11- -4  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,66228,-7622800]	[a1,a2,a3,a4,a6]
Generators	[133:1881:1]	Generators of the group modulo torsion
j	168105213359/228637728	j-invariant
L	2.6998614428055	L(r)(E,1)/r!
Ω	0.19193377070808	Real period
R	3.5166576377429	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	6336cd2 198e2 2112d2 69696dq2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 6336bg2

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

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Quadratic twists for elliptic curve 6336bg2

-4	8	-3	-11
6336cd2	198e2	2112d2	69696dq2

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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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