Cremona's table of elliptic curves

425 = 5² · 17

Field	Data	Notes
Atkin-Lehner	5+ 17+	Signs for the Atkin-Lehner involutions
Class	425d	Isogeny class
Conductor	425	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	6640625 = 58 · 17	Discriminant
Eigenvalues	-1 -2 5+  2  2 -2 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-213,-1208]	[a1,a2,a3,a4,a6]
Generators	[-9:5:1]	Generators of the group modulo torsion
j	68417929/425	j-invariant
L	1.0183803086926	L(r)(E,1)/r!
Ω	1.2501339246714	Real period
R	1.6292339382124	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	6800l1 27200i1 3825h1 85a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 425d1

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

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Quadratic twists for elliptic curve 425d1

-4	8	-3	5	-7	-11	13	17
6800l1	27200i1	3825h1	85a1	20825s1	51425s1	71825d1	7225e1

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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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