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	38025k	Isogeny class
Conductor	38025	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	8640	Modular degree for the optimal curve
Δ	83160675 = 39 · 52 · 132	Discriminant
Eigenvalues	-1 3+ 5+  2  1 13+  4  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-110,82]	[a1,a2,a3,a4,a6]
Generators	[13:20:1]	Generators of the group modulo torsion
j	1755	j-invariant
L	3.8840202838517	L(r)(E,1)/r!
Ω	1.6488442182965	Real period
R	1.1778008621901	Regulator
r	1	Rank of the group of rational points
S	0.99999999999954	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	38025h1 38025v1 38025j1	Quadratic twists by: -3 5 13

Hecke Eigenvalues for elliptic curve 38025k1

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	1	+	4	0	-9	2	-8	1	6	8	-8	-2	12	-7	2	-15	9	0	-1	4	13

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Quadratic twists for elliptic curve 38025k1

-3	5	13
38025h1	38025v1	38025j1

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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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