Cremona's table of elliptic curves

425 = 5² · 17

Field	Data	Notes
Atkin-Lehner	5+ 17+	Signs for the Atkin-Lehner involutions
Class	425a	Isogeny class
Conductor	425	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-1305015625 = -1 · 56 · 174	Discriminant
Eigenvalues	1  0 5+ -4  0  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-17,-1734]	[a1,a2,a3,a4,a6]
Generators	[14:18:1]	Generators of the group modulo torsion
j	-35937/83521	j-invariant
L	2.0769440878185	L(r)(E,1)/r!
Ω	0.69187509911079	Real period
R	1.5009530553187	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	6800h4 27200c3 3825i4 17a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 425a4

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

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Quadratic twists for elliptic curve 425a4

-4	8	-3	5	-7	-11	13	17
6800h4	27200c3	3825i4	17a1	20825o4	51425u3	71825h3	7225b4

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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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