Cremona's table of elliptic curves

325 = 5² · 13

Field	Data	Notes
Atkin-Lehner	5+ 13+	Signs for the Atkin-Lehner involutions
Class	325b	Isogeny class
Conductor	325	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	12	Modular degree for the optimal curve
Δ	325 = 52 · 13	Discriminant
Eigenvalues	0 -1 5+  4 -6 13+ -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-3,3]	[a1,a2,a3,a4,a6]
Generators	[1:0:1]	Generators of the group modulo torsion
j	163840/13	j-invariant
L	1.3630614805608	L(r)(E,1)/r!
Ω	5.3009854471846	Real period
R	0.25713360169377	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	5200q1 20800x1 2925e1 325a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 325b1

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
0	-1	+	4	-6	+	-6	-4	-3	-3	-4	-2	6	7	0	9	-6	-1	-14	-6	4	11	6	0	10

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Quadratic twists for elliptic curve 325b1

-4	8	-3	5	-7	-11	13	17	-19
5200q1	20800x1	2925e1	325a1	15925l1	39325i1	4225a1	93925a1	117325h1

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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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