Cremona's table of elliptic curves

325 = 5² · 13

Field	Data	Notes
Atkin-Lehner	5- 13+	Signs for the Atkin-Lehner involutions
Class	325d	Isogeny class
Conductor	325	Conductor
∏ cp	3	Product of Tamagawa factors cp
Δ	145036328125 = 58 · 135	Discriminant
Eigenvalues	2  1 5-  2  2 13+  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-2458,42369]	[a1,a2,a3,a4,a6]
j	4206161920/371293	j-invariant
L	3.0163634988532	L(r)(E,1)/r!
Ω	1.0054544996177	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5200bf2 20800bx2 2925r2 325e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 325d2

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
2	1	-	2	2	+	2	0	-9	5	2	-8	12	1	-8	11	0	-13	2	12	6	15	-4	-10	-8

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Quadratic twists for elliptic curve 325d2

-4	8	-3	5	-7	-11	13	17	-19
5200bf2	20800bx2	2925r2	325e1	15925y2	39325w2	4225i2	93925q2	117325w2

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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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