Cremona's table of elliptic curves

3850 = 2 · 5² · 7 · 11

Field	Data	Notes
Atkin-Lehner	2+ 5+ 7+ 11+	Signs for the Atkin-Lehner involutions
Class	3850b	Isogeny class
Conductor	3850	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	38880	Modular degree for the optimal curve
Δ	-362024094924800 = -1 · 218 · 52 · 73 · 115	Discriminant
Eigenvalues	2+ -1 5+ 7+ 11+ -2 -3  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-515720,142338880]	[a1,a2,a3,a4,a6]
Generators	[464:1560:1]	Generators of the group modulo torsion
j	-606773969327363726065/14480963796992	j-invariant
L	1.9977102482733	L(r)(E,1)/r!
Ω	0.49763808341324	Real period
R	2.007191887899	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	30800bs1 123200r1 34650cy1 3850y1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3850b1

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	-3	8	0	-6	11	7	6	7	-9	-3	-3	-10	-8	6	-5	-1	-6	0	10

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Quadratic twists for elliptic curve 3850b1

-4	8	-3	5	-7	-11
30800bs1	123200r1	34650cy1	3850y1	26950h1	42350cj1

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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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