Cremona's table of elliptic curves

111296 = 2⁶ · 37 · 47

Field	Data	Notes
Atkin-Lehner	2- 37+ 47+	Signs for the Atkin-Lehner involutions
Class	111296f	Isogeny class
Conductor	111296	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	50304	Modular degree for the optimal curve
Δ	83694592 = 210 · 37 · 472	Discriminant
Eigenvalues	2-  0 -4 -4 -4 -4 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-112,120]	[a1,a2,a3,a4,a6]
Generators	[-6:24:1] [1:3:1]	Generators of the group modulo torsion
j	151732224/81733	j-invariant
L	5.7761345459267	L(r)(E,1)/r!
Ω	1.677413277987	Real period
R	3.4434772982407	Regulator
r	2	Rank of the group of rational points
S	1.0000000005905	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	111296c1 27824c1	Quadratic twists by: -4 8

Hecke Eigenvalues for elliptic curve 111296f1

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	-4	-4	-4	-4	-6	4	-4	4	4	+	10	-4	+	6	14	2	-12	-16	10	-10	-12	6	10

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Quadratic twists for elliptic curve 111296f1

-4	8
111296c1	27824c1

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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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