Cremona's table of elliptic curves

825 = 3 · 5² · 11

Field	Data	Notes
Atkin-Lehner	3+ 5+ 11+	Signs for the Atkin-Lehner involutions
Class	825a	Isogeny class
Conductor	825	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	72	Modular degree for the optimal curve
Δ	-81675 = -1 · 33 · 52 · 112	Discriminant
Eigenvalues	0 3+ 5+  1 11+  1  6 -7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-23,53]	[a1,a2,a3,a4,a6]
Generators	[1:5:1]	Generators of the group modulo torsion
j	-56197120/3267	j-invariant
L	1.8040304299532	L(r)(E,1)/r!
Ω	3.3747765339753	Real period
R	0.26728146468236	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13200ch1 52800cs1 2475i1 825c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 825a1

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
0	+	+	1	+	1	6	-7	-6	-6	-7	-2	-6	1	0	6	0	5	-5	-12	-14	-4	6	6	-17

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Quadratic twists for elliptic curve 825a1

-4	8	-3	5	-7	-11
13200ch1	52800cs1	2475i1	825c1	40425ca1	9075f1

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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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