Cremona's table of elliptic curves

3825 = 3² · 5² · 17

Field	Data	Notes
Atkin-Lehner	3+ 5+ 17+	Signs for the Atkin-Lehner involutions
Class	3825b	Isogeny class
Conductor	3825	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	3360	Modular degree for the optimal curve
Δ	-5228296875 = -1 · 39 · 56 · 17	Discriminant
Eigenvalues	-2 3+ 5+  2  3  5 17+ -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-675,-7594]	[a1,a2,a3,a4,a6]
Generators	[36:121:1]	Generators of the group modulo torsion
j	-110592/17	j-invariant
L	2.1284189804971	L(r)(E,1)/r!
Ω	0.46438602772509	Real period
R	2.2916483845602	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	61200df1 3825d1 153d1 65025m1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 3825b1

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
-2	+	+	2	3	5	+	-1	-7	-6	4	-10	-9	-1	-12	-12	-6	2	-4	8	0	-6	4	-2	-8

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Quadratic twists for elliptic curve 3825b1

-4	-3	5	17
61200df1	3825d1	153d1	65025m1

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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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