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	525c	Isogeny class
Conductor	525	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	240	Modular degree for the optimal curve
Δ	369140625 = 33 · 59 · 7	Discriminant
Eigenvalues	1 3+ 5- 7- -6  2 -4 -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-450,3375]	[a1,a2,a3,a4,a6]
Generators	[14:1:1]	Generators of the group modulo torsion
j	5177717/189	j-invariant
L	2.1137948118601	L(r)(E,1)/r!
Ω	1.6844284064271	Real period
R	2.5098066546429	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	8400cr1 33600dz1 1575j1 525d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 525c1

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	+	-	-	-6	2	-4	-6	0	-2	-10	4	2	4	0	-6	-8	-2	16	10	6	4	-8	6	2

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Quadratic twists for elliptic curve 525c1

-4	8	-3	5	-7	-11	13
8400cr1	33600dz1	1575j1	525d1	3675p1	63525z1	88725bf1

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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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