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	3038d	Isogeny class
Conductor	3038	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	44319790088 = 23 · 78 · 312	Discriminant
Eigenvalues	2+  0  0 7- -2  2 -2  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-2312,-41000]	[a1,a2,a3,a4,a6]
Generators	[79:475:1]	Generators of the group modulo torsion
j	11619959625/376712	j-invariant
L	2.4114880741474	L(r)(E,1)/r!
Ω	0.68985284124408	Real period
R	1.7478278916693	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	24304l2 97216o2 27342bm2 75950cm2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3038d2

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
+	0	0	-	-2	2	-2	6	0	8	-	-8	10	-6	4	4	-6	-6	-4	-8	-14	-16	-8	6	-14

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Quadratic twists for elliptic curve 3038d2

-4	8	-3	5	-7	-31
24304l2	97216o2	27342bm2	75950cm2	434a2	94178d2

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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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