Cremona's table of elliptic curves

41184 = 2⁵ · 3² · 11 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3+ 11+ 13+	Signs for the Atkin-Lehner involutions
Class	41184a	Isogeny class
Conductor	41184	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	22528	Modular degree for the optimal curve
Δ	-5971762368 = -1 · 26 · 33 · 112 · 134	Discriminant
Eigenvalues	2+ 3+  0  4 11+ 13+ -4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,315,-3032]	[a1,a2,a3,a4,a6]
Generators	[11:42:1]	Generators of the group modulo torsion
j	2000376000/3455881	j-invariant
L	6.5518502625568	L(r)(E,1)/r!
Ω	0.70679652801745	Real period
R	2.3174456872815	Regulator
r	1	Rank of the group of rational points
S	0.99999999999976	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	41184e1 82368dd2 41184u1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 41184a1

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

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Quadratic twists for elliptic curve 41184a1

-4	8	-3
41184e1	82368dd2	41184u1

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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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