Cremona's table of elliptic curves

63525 = 3 · 5² · 7 · 11²

Field	Data	Notes
Atkin-Lehner	3- 5+ 7+ 11-	Signs for the Atkin-Lehner involutions
Class	63525bj	Isogeny class
Conductor	63525	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	737280	Modular degree for the optimal curve
Δ	351682539140625 = 3 · 57 · 7 · 118	Discriminant
Eigenvalues	-1 3- 5+ 7+ 11- -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-801688,-276349633]	[a1,a2,a3,a4,a6]
Generators	[9882491:-393374158:4913]	Generators of the group modulo torsion
j	2058561081361/12705	j-invariant
L	3.7948719253175	L(r)(E,1)/r!
Ω	0.15955057252714	Real period
R	11.892379530352	Regulator
r	1	Rank of the group of rational points
S	0.99999999993733	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	12705g1 5775u1	Quadratic twists by: 5 -11

Hecke Eigenvalues for elliptic curve 63525bj1

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	-6	4	-8	-6	8	-6	6	-4	8	10	-12	10	12	-8	-6	-8	-4	10	14

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Quadratic twists for elliptic curve 63525bj1

5	-11
12705g1	5775u1

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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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