Cremona's table of elliptic curves

3844 = 2² · 31²

Field	Data	Notes
Atkin-Lehner	2- 31-	Signs for the Atkin-Lehner involutions
Class	3844d	Isogeny class
Conductor	3844	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-476656 = -1 · 24 · 313	Discriminant
Eigenvalues	2- -2  1 -1  4 -2 -2 -5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-10,-39]	[a1,a2,a3,a4,a6]
Generators	[10:31:1]	Generators of the group modulo torsion
j	-256	j-invariant
L	2.6439002871485	L(r)(E,1)/r!
Ω	1.2162636779875	Real period
R	0.36229812320566	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	15376w1 61504t1 34596j1 96100d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3844d1

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	-1	4	-2	-2	-5	6	6	-	8	-5	-10	-8	4	9	-14	8	9	4	-10	-4	14	-7

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Quadratic twists for elliptic curve 3844d1

-4	8	-3	5	-31
15376w1	61504t1	34596j1	96100d1	3844b1

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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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