Cremona's table of elliptic curves

13490 = 2 · 5 · 19 · 71

Field	Data	Notes
Atkin-Lehner	2+ 5- 19+ 71-	Signs for the Atkin-Lehner involutions
Class	13490b	Isogeny class
Conductor	13490	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	12928	Modular degree for the optimal curve
Δ	-119723750 = -1 · 2 · 54 · 19 · 712	Discriminant
Eigenvalues	2+ -3 5-  3  2  1 -7 19+	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-679,7003]	[a1,a2,a3,a4,a6]
Generators	[37:159:1]	Generators of the group modulo torsion
j	-34649164377801/119723750	j-invariant
L	2.5255969724937	L(r)(E,1)/r!
Ω	1.8717576535247	Real period
R	0.16866479534208	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	107920n1 121410s1 67450n1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 13490b1

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
+	-3	-	3	2	1	-7	+	3	-1	-10	6	2	6	12	5	-9	-4	-5	-	-3	8	-4	-8	-6

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Quadratic twists for elliptic curve 13490b1

-4	-3	5
107920n1	121410s1	67450n1

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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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