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	525b	Isogeny class
Conductor	525	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	717609375 = 38 · 56 · 7	Discriminant
Eigenvalues	1 3+ 5+ 7-  4  2  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-975,11250]	[a1,a2,a3,a4,a6]
j	6570725617/45927	j-invariant
L	1.6139595394337	L(r)(E,1)/r!
Ω	1.6139595394337	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	8400cd3 33600dd3 1575g3 21a3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 525b4

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	2	6	4	0	-2	0	-6	2	4	0	-6	12	-2	-4	0	6	-16	12	-14	-18

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Quadratic twists for elliptic curve 525b4

-4	8	-3	5	-7	-11	13
8400cd3	33600dd3	1575g3	21a3	3675j3	63525i3	88725h3

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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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