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	41952d	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	[47:-276:1]	Generators of the group modulo torsion
j	-2650991104/90459	j-invariant
L	3.7961859071915	L(r)(E,1)/r!
Ω	0.51403808486691	Real period
R	0.92312856258929	Regulator
r	1	Rank of the group of rational points
S	0.99999999999914	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	41952g1 83904bm1 125856bg1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 41952d1

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 41952d1

-4	8	-3
41952g1	83904bm1	125856bg1

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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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