Cremona's table of elliptic curves

11424 = 2⁵ · 3 · 7 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 17+	Signs for the Atkin-Lehner involutions
Class	11424s	Isogeny class
Conductor	11424	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	36864	Modular degree for the optimal curve
Δ	458449420290624 = 26 · 36 · 76 · 174	Discriminant
Eigenvalues	2- 3- -2 7+  4  2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-34014,2172456]	[a1,a2,a3,a4,a6]
Generators	[150:684:1]	Generators of the group modulo torsion
j	68003243639904448/7163272192041	j-invariant
L	4.9814454747853	L(r)(E,1)/r!
Ω	0.51116050007508	Real period
R	3.2484548878181	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	11424n1 22848bt2 34272m1 79968bv1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 11424s1

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
-	-	-2	+	4	2	+	4	-4	-2	-8	-2	-2	-8	0	6	-4	2	8	-4	-6	0	4	6	10

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Quadratic twists for elliptic curve 11424s1

-4	8	-3	-7
11424n1	22848bt2	34272m1	79968bv1

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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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