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
Δ	54925 = 52 · 133	Discriminant
Eigenvalues	0 -1 5+  4 -6 13+ -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-53,-132]	[a1,a2,a3,a4,a6]
Generators	[-4:0:1]	Generators of the group modulo torsion
j	671088640/2197	j-invariant
L	1.3630614805608	L(r)(E,1)/r!
Ω	1.7669951490615	Real period
R	0.7714008050813	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	5200q2 20800x2 2925e2 325a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 325b2

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 325b2

-4	8	-3	5	-7	-11	13	17	-19
5200q2	20800x2	2925e2	325a2	15925l2	39325i2	4225a2	93925a2	117325h2

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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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