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	11712w	Isogeny class
Conductor	11712	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-316224 = -1 · 26 · 34 · 61	Discriminant
Eigenvalues	2- 3+  3  3 -1  3 -2  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,16,-18]	[a1,a2,a3,a4,a6]
j	6644672/4941	j-invariant
L	3.4233516813842	L(r)(E,1)/r!
Ω	1.7116758406921	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	11712bj1 5856h1 35136cg1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 11712w1

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	-1	3	-2	6	9	8	8	2	-7	0	0	6	1	+	-7	4	-11	1	-4	-12	-2

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Quadratic twists for elliptic curve 11712w1

-4	8	-3
11712bj1	5856h1	35136cg1

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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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