Cremona's table of elliptic curves

42016 = 2⁵ · 13 · 101

Field	Data	Notes
Atkin-Lehner	2+ 13- 101+	Signs for the Atkin-Lehner involutions
Class	42016b	Isogeny class
Conductor	42016	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	5632	Modular degree for the optimal curve
Δ	-5378048 = -1 · 212 · 13 · 101	Discriminant
Eigenvalues	2+  1  0 -2 -4 13-  3  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-33,-145]	[a1,a2,a3,a4,a6]
Generators	[7:4:1] [10:25:1]	Generators of the group modulo torsion
j	-1000000/1313	j-invariant
L	9.9202217399705	L(r)(E,1)/r!
Ω	0.94720787386714	Real period
R	2.6182800031712	Regulator
r	2	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	42016e1 84032e1	Quadratic twists by: -4 8

Hecke Eigenvalues for elliptic curve 42016b1

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	0	-2	-4	-	3	1	-6	-10	-4	-8	-5	-8	-8	-10	8	-4	-12	3	15	-8	6	15	0

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Quadratic twists for elliptic curve 42016b1

-4	8
42016e1	84032e1

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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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