Cremona's table of elliptic curves

56784 = 2⁴ · 3 · 7 · 13²

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 13+	Signs for the Atkin-Lehner involutions
Class	56784bw	Isogeny class
Conductor	56784	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	55296	Modular degree for the optimal curve
Δ	-102173892912 = -1 · 24 · 33 · 72 · 136	Discriminant
Eigenvalues	2- 3+  0 7- -6 13+  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,1127,4588]	[a1,a2,a3,a4,a6]
Generators	[618:5915:8]	Generators of the group modulo torsion
j	2048000/1323	j-invariant
L	4.5013494823147	L(r)(E,1)/r!
Ω	0.66283294697137	Real period
R	3.3955384255618	Regulator
r	1	Rank of the group of rational points
S	0.99999999999454	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	14196h1 336a1	Quadratic twists by: -4 13

Hecke Eigenvalues for elliptic curve 56784bw1

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

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Quadratic twists for elliptic curve 56784bw1

-4	13
14196h1	336a1

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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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