Cremona's table of elliptic curves

1325 = 5² · 53

Field	Data	Notes
Atkin-Lehner	5+ 53-	Signs for the Atkin-Lehner involutions
Class	1325b	Isogeny class
Conductor	1325	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-685791015625 = -1 · 512 · 532	Discriminant
Eigenvalues	1  0 5+ -2  0  6  6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-3317,84466]	[a1,a2,a3,a4,a6]
j	-258353141409/43890625	j-invariant
L	1.7449219911937	L(r)(E,1)/r!
Ω	0.87246099559683	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	21200o2 84800a2 11925o2 265a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1325b2

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	0	+	-2	0	6	6	-2	8	2	10	-2	-6	2	2	-	4	10	0	-2	-14	-10	-8	-2	-10

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Quadratic twists for elliptic curve 1325b2

-4	8	-3	5	-7	53
21200o2	84800a2	11925o2	265a2	64925h2	70225c2

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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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