Cremona's table of elliptic curves

14784 = 2⁶ · 3 · 7 · 11

Field	Data	Notes
Atkin-Lehner	2+ 3- 7+ 11-	Signs for the Atkin-Lehner involutions
Class	14784z	Isogeny class
Conductor	14784	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	12288	Modular degree for the optimal curve
Δ	-71939653632 = -1 · 220 · 34 · 7 · 112	Discriminant
Eigenvalues	2+ 3-  0 7+ 11-  2 -4 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,287,-12673]	[a1,a2,a3,a4,a6]
Generators	[41:264:1]	Generators of the group modulo torsion
j	9938375/274428	j-invariant
L	5.6745829298422	L(r)(E,1)/r!
Ω	0.52843300407341	Real period
R	1.3423137100872	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	14784bx1 462a1 44352o1 103488bm1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 14784z1

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	+	-	2	-4	-6	-4	10	6	6	-12	8	2	-6	8	-6	4	0	-12	0	-14	10	10

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Quadratic twists for elliptic curve 14784z1

-4	8	-3	-7
14784bx1	462a1	44352o1	103488bm1

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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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