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	3038i	Isogeny class
Conductor	3038	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-58353904 = -1 · 24 · 76 · 31	Discriminant
Eigenvalues	2-  0  2 7-  0 -2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-34,-367]	[a1,a2,a3,a4,a6]
j	-35937/496	j-invariant
L	3.3852136029281	L(r)(E,1)/r!
Ω	0.84630340073201	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	24304n1 97216s1 27342q1 75950t1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3038i1

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	2	-	0	-2	6	-4	8	2	-	10	6	8	8	-6	12	6	-12	8	-10	-8	-8	6	-2

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Quadratic twists for elliptic curve 3038i1

-4	8	-3	5	-7	-31
24304n1	97216s1	27342q1	75950t1	62a1	94178u1

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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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