Cremona's table of elliptic curves

27456 = 2⁶ · 3 · 11 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3+ 11+ 13+	Signs for the Atkin-Lehner involutions
Class	27456a	Isogeny class
Conductor	27456	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	123830464462848 = 214 · 37 · 112 · 134	Discriminant
Eigenvalues	2+ 3+  2 -2 11+ 13+  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-44177,3548337]	[a1,a2,a3,a4,a6]
Generators	[-227:1352:1]	Generators of the group modulo torsion
j	581972233018192/7558011747	j-invariant
L	4.5219539896083	L(r)(E,1)/r!
Ω	0.58965491626003	Real period
R	1.9172035477502	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	27456ce2 1716c2 82368bw2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 27456a2

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

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Quadratic twists for elliptic curve 27456a2

-4	8	-3
27456ce2	1716c2	82368bw2

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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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