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	21	Product of Tamagawa factors cp
Δ	84775503032064 = 28 · 37 · 133 · 413	Discriminant
Eigenvalues	2- 3- -3  2  3 13-  3  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-2748532,-1754794156]	[a1,a2,a3,a4,a6]
j	8969873074652230258768/331154308719	j-invariant
L	2.4623151533799	L(r)(E,1)/r!
Ω	0.1172531025419	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	25584r2 102336c2 19188s2 83148m2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 6396f2

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 6396f2

-4	8	-3	13
25584r2	102336c2	19188s2	83148m2

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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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