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	3850a	Isogeny class
Conductor	3850	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	288	Modular degree for the optimal curve
Δ	-7700 = -1 · 22 · 52 · 7 · 11	Discriminant
Eigenvalues	2+  1 5+ 7+ 11+  2  7 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,4,-2]	[a1,a2,a3,a4,a6]
Generators	[1:1:1]	Generators of the group modulo torsion
j	397535/308	j-invariant
L	2.9916814507841	L(r)(E,1)/r!
Ω	2.3214678312888	Real period
R	0.64435126140067	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	30800bu1 123200u1 34650cw1 3850z1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3850a1

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	7	-4	-8	6	5	-1	2	-13	1	-11	3	10	4	-10	1	-5	-14	4	2

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Quadratic twists for elliptic curve 3850a1

-4	8	-3	5	-7	-11
30800bu1	123200u1	34650cw1	3850z1	26950m1	42350cf1

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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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