Cremona's table of elliptic curves

41952 = 2⁵ · 3 · 19 · 23

Field	Data	Notes
Atkin-Lehner	2+ 3- 19+ 23+	Signs for the Atkin-Lehner involutions
Class	41952g	Isogeny class
Conductor	41952	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	18432	Modular degree for the optimal curve
Δ	-370520064 = -1 · 212 · 32 · 19 · 232	Discriminant
Eigenvalues	2+ 3- -1  1 -5 -6 -3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-461,3771]	[a1,a2,a3,a4,a6]
Generators	[13:12:1] [22:69:1]	Generators of the group modulo torsion
j	-2650991104/90459	j-invariant
L	10.017954407897	L(r)(E,1)/r!
Ω	1.6870228292067	Real period
R	0.74228058998805	Regulator
r	2	Rank of the group of rational points
S	1.0000000000002	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	41952d1 83904bf1 125856ba1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 41952g1

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
+	-	-1	1	-5	-6	-3	+	+	-6	-4	-12	-2	5	-9	12	-8	5	-12	-10	-11	-10	4	8	-6

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Quadratic twists for elliptic curve 41952g1

-4	8	-3
41952d1	83904bf1	125856ba1

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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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