Cremona's table of elliptic curves

25536 = 2⁶ · 3 · 7 · 19

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 19+	Signs for the Atkin-Lehner involutions
Class	25536cs	Isogeny class
Conductor	25536	Conductor
∏ cp	40	Product of Tamagawa factors cp
Δ	116222077698048 = 219 · 35 · 7 · 194	Discriminant
Eigenvalues	2- 3-  2 7+ -4  2 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1161697,-482320993]	[a1,a2,a3,a4,a6]
Generators	[8402:763515:1]	Generators of the group modulo torsion
j	661397832743623417/443352042	j-invariant
L	7.0455431168599	L(r)(E,1)/r!
Ω	0.14542073120545	Real period
R	4.8449372097478	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	25536t4 6384t3 76608dy4	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 25536cs4

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
-	-	2	+	-4	2	-2	+	4	-2	-4	6	-10	-4	8	-10	12	2	-8	16	10	8	0	-10	-2

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Quadratic twists for elliptic curve 25536cs4

-4	8	-3
25536t4	6384t3	76608dy4

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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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