Cremona's table of elliptic curves

5856 = 2⁵ · 3 · 61

Field	Data	Notes
Atkin-Lehner	2+ 3+ 61-	Signs for the Atkin-Lehner involutions
Class	5856b	Isogeny class
Conductor	5856	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	864	Modular degree for the optimal curve
Δ	-843264 = -1 · 29 · 33 · 61	Discriminant
Eigenvalues	2+ 3+  3  2  2 -4  3  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-24,72]	[a1,a2,a3,a4,a6]
j	-3112136/1647	j-invariant
L	2.6197743725093	L(r)(E,1)/r!
Ω	2.6197743725093	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5856f1 11712bk1 17568o1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 5856b1

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	2	-4	3	8	-1	-6	0	1	8	11	-8	2	0	-	4	11	-17	6	9	15	-1

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Quadratic twists for elliptic curve 5856b1

-4	8	-3
5856f1	11712bk1	17568o1

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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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