Cremona's table of elliptic curves

6396 = 2² · 3 · 13 · 41

Field	Data	Notes
Atkin-Lehner	2- 3- 13- 41+	Signs for the Atkin-Lehner involutions
Class	6396f	Isogeny class
Conductor	6396	Conductor
∏ cp	63	Product of Tamagawa factors cp
deg	31248	Modular degree for the optimal curve
Δ	1427294273842944 = 28 · 321 · 13 · 41	Discriminant
Eigenvalues	2- 3- -3  2  3 13-  3  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-36652,-2009884]	[a1,a2,a3,a4,a6]
j	21271035361447888/5575368257199	j-invariant
L	2.4623151533799	L(r)(E,1)/r!
Ω	0.3517593076257	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	25584r1 102336c1 19188s1 83148m1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 6396f1

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
-	-	-3	2	3	-	3	2	9	-3	-7	2	+	2	-3	9	6	-1	2	0	-10	-1	-12	-12	-1

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Quadratic twists for elliptic curve 6396f1

-4	8	-3	13
25584r1	102336c1	19188s1	83148m1

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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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