Cremona's table of elliptic curves

325 = 5² · 13

Field	Data	Notes
Atkin-Lehner	5+ 13-	Signs for the Atkin-Lehner involutions
Class	325c	Isogeny class
Conductor	325	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	1015625 = 57 · 13	Discriminant
Eigenvalues	1  2 5+  4  2 13- -2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-25,0]	[a1,a2,a3,a4,a6]
j	117649/65	j-invariant
L	2.4072852546238	L(r)(E,1)/r!
Ω	2.4072852546238	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	5200bb1 20800o1 2925k1 65a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 325c1

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	+	4	2	-	-2	-6	6	2	-10	2	-6	-10	-4	-2	6	2	4	6	6	-12	16	2	2

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Quadratic twists for elliptic curve 325c1

-4	8	-3	5	-7	-11	13	17	-19
5200bb1	20800o1	2925k1	65a1	15925f1	39325d1	4225b1	93925i1	117325c1

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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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