Cremona's table of elliptic curves

11712 = 2⁶ · 3 · 61

Field	Data	Notes
Atkin-Lehner	2+ 3- 61+	Signs for the Atkin-Lehner involutions
Class	11712i	Isogeny class
Conductor	11712	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	-80953344 = -1 · 214 · 34 · 61	Discriminant
Eigenvalues	2+ 3- -1 -5 -5 -1 -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-401,2991]	[a1,a2,a3,a4,a6]
Generators	[-17:72:1] [7:24:1]	Generators of the group modulo torsion
j	-436334416/4941	j-invariant
L	6.2367834525943	L(r)(E,1)/r!
Ω	1.933479062083	Real period
R	0.20160495835275	Regulator
r	2	Rank of the group of rational points
S	0.99999999999998	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	11712r1 732b1 35136m1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 11712i1

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	-5	-5	-1	-6	2	-7	-4	-8	-6	-7	8	-8	6	-3	+	-3	-12	13	9	0	0	-10

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Quadratic twists for elliptic curve 11712i1

-4	8	-3
11712r1	732b1	35136m1

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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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