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	8	Product of Tamagawa factors cp
Δ	-2822265625 = -1 · 510 · 172	Discriminant
Eigenvalues	-1 -2 5+  2  2 -2 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-88,-2583]	[a1,a2,a3,a4,a6]
Generators	[37:194:1]	Generators of the group modulo torsion
j	-4826809/180625	j-invariant
L	1.0183803086926	L(r)(E,1)/r!
Ω	0.62506696233568	Real period
R	0.81461696910621	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	6800l2 27200i2 3825h2 85a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 425d2

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 425d2

-4	8	-3	5	-7	-11	13	17
6800l2	27200i2	3825h2	85a2	20825s2	51425s2	71825d2	7225e2

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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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