Cremona's table of elliptic curves

88725 = 3 · 5² · 7 · 13²

Field	Data	Notes
Atkin-Lehner	3+ 5+ 7+ 13+	Signs for the Atkin-Lehner involutions
Class	88725f	Isogeny class
Conductor	88725	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	1264701262362890625 = 34 · 58 · 72 · 138	Discriminant
Eigenvalues	1 3+ 5+ 7+ -4 13+ -6 -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-1155625,-475571000]	[a1,a2,a3,a4,a6]
Generators	[-5218:11483:8]	Generators of the group modulo torsion
j	2263054145689/16769025	j-invariant
L	3.6472696666295	L(r)(E,1)/r!
Ω	0.14567642353713	Real period
R	6.2591968762886	Regulator
r	1	Rank of the group of rational points
S	1.0000000016504	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	17745w2 6825d2	Quadratic twists by: 5 13

Hecke Eigenvalues for elliptic curve 88725f2

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
1	+	+	+	-4	+	-6	-8	4	-2	4	10	2	-8	8	-6	-8	-10	-12	8	6	8	-4	-6	-2

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Quadratic twists for elliptic curve 88725f2

5	13
17745w2	6825d2

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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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