Cremona's table of elliptic curves

3038 = 2 · 7² · 31

Field	Data	Notes
Atkin-Lehner	2- 7- 31+	Signs for the Atkin-Lehner involutions
Class	3038h	Isogeny class
Conductor	3038	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-294348813616466 = -1 · 2 · 715 · 31	Discriminant
Eigenvalues	2- -1 -3 7-  0  4  6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-165327,25818295]	[a1,a2,a3,a4,a6]
Generators	[10324:112455:64]	Generators of the group modulo torsion
j	-4247828669470177/2501923634	j-invariant
L	3.5514187637799	L(r)(E,1)/r!
Ω	0.54054010086191	Real period
R	1.6425325142931	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	24304v3 97216h3 27342k3 75950j3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3038h3

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	-	0	4	6	-2	-3	3	+	2	-12	-10	-3	6	0	-8	-13	-12	-11	-1	9	9	-8

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Quadratic twists for elliptic curve 3038h3

-4	8	-3	5	-7	-31
24304v3	97216h3	27342k3	75950j3	434b3	94178x3

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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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