Cremona's table of elliptic curves

20064 = 2⁵ · 3 · 11 · 19

Field	Data	Notes
Atkin-Lehner	2+ 3- 11- 19+	Signs for the Atkin-Lehner involutions
Class	20064k	Isogeny class
Conductor	20064	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	9280	Modular degree for the optimal curve
Δ	-321024 = -1 · 29 · 3 · 11 · 19	Discriminant
Eigenvalues	2+ 3-  3 -2 11- -4  7 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1464,-22056]	[a1,a2,a3,a4,a6]
Generators	[324190:2043534:4913]	Generators of the group modulo torsion
j	-678224691656/627	j-invariant
L	7.2973411470469	L(r)(E,1)/r!
Ω	0.38588646665705	Real period
R	9.4552955047427	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	20064e1 40128bl1 60192r1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 20064k1

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	-2	-	-4	7	+	0	-7	-2	-11	-2	1	-8	2	8	5	-3	-8	12	-16	-2	-9	-12

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Quadratic twists for elliptic curve 20064k1

-4	8	-3
20064e1	40128bl1	60192r1

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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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