Cremona's table of elliptic curves

3800 = 2³ · 5² · 19

Field	Data	Notes
Atkin-Lehner	2- 5+ 19-	Signs for the Atkin-Lehner involutions
Class	3800g	Isogeny class
Conductor	3800	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	-608000000 = -1 · 211 · 56 · 19	Discriminant
Eigenvalues	2- -1 5+ -3  2 -1  5 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-208,-1588]	[a1,a2,a3,a4,a6]
Generators	[37:200:1]	Generators of the group modulo torsion
j	-31250/19	j-invariant
L	2.7045961358503	L(r)(E,1)/r!
Ω	0.61137014988028	Real period
R	2.21191379427	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	7600a1 30400e1 34200bf1 152b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3800g1

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	+	-3	2	-1	5	-	1	-3	4	-2	-8	8	8	-9	1	14	-13	10	-9	-10	-10	-12	-14

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Quadratic twists for elliptic curve 3800g1

-4	8	-3	5	-19
7600a1	30400e1	34200bf1	152b1	72200f1

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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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