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	3850bb	Isogeny class
Conductor	3850	Conductor
∏ cp	324	Product of Tamagawa factors cp
deg	5184	Modular degree for the optimal curve
Δ	-1022633920000 = -1 · 29 · 54 · 74 · 113	Discriminant
Eigenvalues	2- -2 5- 7- 11- -1  0 -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1113,50617]	[a1,a2,a3,a4,a6]
Generators	[-42:175:1]	Generators of the group modulo torsion
j	-243979633825/1636214272	j-invariant
L	3.8859462242512	L(r)(E,1)/r!
Ω	0.75455331985515	Real period
R	0.14305543138338	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	30800ce1 123200dd1 34650bw1 3850e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3850bb1

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	-	-	-	-1	0	-1	-9	-3	5	-4	0	-1	0	-6	0	2	2	-9	-4	-4	-9	15	-1

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Quadratic twists for elliptic curve 3850bb1

-4	8	-3	5	-7	-11
30800ce1	123200dd1	34650bw1	3850e1	26950di1	42350bo1

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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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