Cremona's table of elliptic curves

1525 = 5² · 61

Field	Data	Notes
Atkin-Lehner	5- 61+	Signs for the Atkin-Lehner involutions
Class	1525c	Isogeny class
Conductor	1525	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	112	Modular degree for the optimal curve
Δ	7625 = 53 · 61	Discriminant
Eigenvalues	-1 -2 5- -4  0 -4 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-8,7]	[a1,a2,a3,a4,a6]
Generators	[-3:4:1] [-2:5:1]	Generators of the group modulo torsion
j	456533/61	j-invariant
L	1.6341045674767	L(r)(E,1)/r!
Ω	4.0135649400233	Real period
R	0.8142908321639	Regulator
r	2	Rank of the group of rational points
S	0.99999999999938	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	24400y1 97600bk1 13725l1 1525b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1525c1

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	-2	-	-4	0	-4	-6	-4	-4	-6	0	-2	-10	-8	-6	-14	4	+	8	12	4	-12	14	6	16

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Quadratic twists for elliptic curve 1525c1

-4	8	-3	5	-7	61
24400y1	97600bk1	13725l1	1525b1	74725u1	93025j1

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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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