Cremona's table of elliptic curves

325 = 5² · 13

Field	Data	Notes
Atkin-Lehner	5- 13-	Signs for the Atkin-Lehner involutions
Class	325a	Isogeny class
Conductor	325	Conductor
∏ cp	3	Product of Tamagawa factors cp
Δ	858203125 = 58 · 133	Discriminant
Eigenvalues	0  1 5- -4 -6 13-  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-1333,-19131]	[a1,a2,a3,a4,a6]
Generators	[-21:6:1]	Generators of the group modulo torsion
j	671088640/2197	j-invariant
L	1.5716909753136	L(r)(E,1)/r!
Ω	0.79022425384279	Real period
R	0.66297255395989	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	5200bh2 20800bk2 2925t2 325b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 325a2

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 325a2

-4	8	-3	5	-7	-11	13	17	-19
5200bh2	20800bk2	2925t2	325b2	15925t2	39325t2	4225h2	93925u2	117325m2

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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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