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	160	Product of Tamagawa factors cp
Δ	1095256255758336 = 220 · 310 · 72 · 192	Discriminant
Eigenvalues	2- 3-  2 7+ -4  2 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-73057,-7456225]	[a1,a2,a3,a4,a6]
Generators	[-139:180:1]	Generators of the group modulo torsion
j	164503536215257/4178071044	j-invariant
L	7.0455431168599	L(r)(E,1)/r!
Ω	0.29084146241089	Real period
R	2.4224686048739	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	25536t2 6384t2 76608dy2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 25536cs2

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 25536cs2

-4	8	-3
25536t2	6384t2	76608dy2

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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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