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	3850c	Isogeny class
Conductor	3850	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-48934630937500 = -1 · 22 · 57 · 76 · 113	Discriminant
Eigenvalues	2+  2 5+ 7+ 11+ -2 -6  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-2250,-340000]	[a1,a2,a3,a4,a6]
Generators	[125:1100:1]	Generators of the group modulo torsion
j	-80677568161/3131816380	j-invariant
L	3.4948283929355	L(r)(E,1)/r!
Ω	0.27729563649256	Real period
R	3.1508144494633	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	30800bz3 123200bc3 34650cz3 770g3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3850c3

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
+	2	+	+	+	-2	-6	2	6	0	8	-8	0	4	0	-12	12	-10	4	-12	-14	-10	0	-18	-8

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Quadratic twists for elliptic curve 3850c3

-4	8	-3	5	-7	-11
30800bz3	123200bc3	34650cz3	770g3	26950o3	42350cp3

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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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