Cremona's table of elliptic curves

425 = 5² · 17

Field	Data	Notes
Atkin-Lehner	5+ 17+	Signs for the Atkin-Lehner involutions
Class	425c	Isogeny class
Conductor	425	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	12	Modular degree for the optimal curve
Δ	-425 = -1 · 52 · 17	Discriminant
Eigenvalues	-1  1 5+ -1 -4  1 17+ -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-3,2]	[a1,a2,a3,a4,a6]
Generators	[1:0:1]	Generators of the group modulo torsion
j	-121945/17	j-invariant
L	1.4080433296718	L(r)(E,1)/r!
Ω	5.1322753273356	Real period
R	0.27435070019962	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	6800k1 27200f1 3825g1 425b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 425c1

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	1	+	-1	-4	1	+	-6	0	0	-7	4	-2	-4	6	-11	8	10	-8	7	-4	-11	8	-6	16

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Quadratic twists for elliptic curve 425c1

-4	8	-3	5	-7	-11	13	17
6800k1	27200f1	3825g1	425b1	20825r1	51425o1	71825b1	7225c1

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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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