Cremona's table of elliptic curves

525 = 3 · 5² · 7

Field	Data	Notes
Atkin-Lehner	3+ 5+ 7+	Signs for the Atkin-Lehner involutions
Class	525a	Isogeny class
Conductor	525	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-15193828125 = -1 · 34 · 57 · 74	Discriminant
Eigenvalues	-1 3+ 5+ 7+  0  6 -2 -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,437,-4594]	[a1,a2,a3,a4,a6]
Generators	[20:102:1]	Generators of the group modulo torsion
j	590589719/972405	j-invariant
L	1.2004647676528	L(r)(E,1)/r!
Ω	0.65555402526641	Real period
R	0.4578054292188	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	8400cg4 33600ce3 1575f4 105a4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 525a4

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	+	+	+	0	6	-2	-8	-8	-2	4	2	-6	-4	-8	-10	4	-2	-4	-12	2	8	4	-6	18

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Quadratic twists for elliptic curve 525a4

-4	8	-3	5	-7	-11	13
8400cg4	33600ce3	1575f4	105a4	3675l4	63525q3	88725s3

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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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