Cremona's table of elliptic curves

38025 = 3² · 5² · 13²

Field	Data	Notes
Atkin-Lehner	3+ 5+ 13+	Signs for the Atkin-Lehner involutions
Class	38025b	Isogeny class
Conductor	38025	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-51975421875 = -1 · 39 · 56 · 132	Discriminant
Eigenvalues	0 3+ 5+ -1  0 13+  0 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,0,-10969]	[a1,a2,a3,a4,a6]
Generators	[210:671:8]	Generators of the group modulo torsion
j	0	j-invariant
L	3.8600397860926	L(r)(E,1)/r!
Ω	0.51523519886157	Real period
R	1.8729503509376	Regulator
r	1	Rank of the group of rational points
S	0.99999999999998	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	38025b1 1521a2 38025a2	Quadratic twists by: -3 5 13

Hecke Eigenvalues for elliptic curve 38025b2

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	0	+	0	-8	0	0	7	-10	0	13	0	0	0	-13	11	0	17	-13	0	0	5

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Quadratic twists for elliptic curve 38025b2

-3	5	13
38025b1	1521a2	38025a2

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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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