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	4515625 = 56 · 172	Discriminant
Eigenvalues	1  0 5+ -4  0  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-142,-609]	[a1,a2,a3,a4,a6]
Generators	[94:853:1]	Generators of the group modulo torsion
j	20346417/289	j-invariant
L	2.0769440878185	L(r)(E,1)/r!
Ω	1.3837501982216	Real period
R	3.0019061106374	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	6800h2 27200c2 3825i2 17a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 425a2

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 425a2

-4	8	-3	5	-7	-11	13	17
6800h2	27200c2	3825i2	17a2	20825o2	51425u2	71825h2	7225b2

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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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