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
deg	64	Modular degree for the optimal curve
Δ	-984375 = -1 · 32 · 56 · 7	Discriminant
Eigenvalues	1 3+ 5+ 7-  4  2  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,25,0]	[a1,a2,a3,a4,a6]
j	103823/63	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	8400cd1 33600dd1 1575g1 21a4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 525b1

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 525b1

-4	8	-3	5	-7	-11	13
8400cd1	33600dd1	1575g1	21a4	3675j1	63525i1	88725h1

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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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