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	11424n	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	[260:2548:1]	Generators of the group modulo torsion
j	68003243639904448/7163272192041	j-invariant
L	3.1385710616866	L(r)(E,1)/r!
Ω	0.3539425577962	Real period
R	2.9558196121133	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	11424s1 22848cs2 34272t1 79968cv1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 11424n1

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 11424n1

-4	8	-3	-7
11424s1	22848cs2	34272t1	79968cv1

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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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