Cremona's table of elliptic curves

9424 = 2⁴ · 19 · 31

Field	Data	Notes
Atkin-Lehner	2- 19+ 31-	Signs for the Atkin-Lehner involutions
Class	9424d	Isogeny class
Conductor	9424	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	-183353344 = -1 · 214 · 192 · 31	Discriminant
Eigenvalues	2-  2  2  0  4 -6 -6 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-192,1280]	[a1,a2,a3,a4,a6]
Generators	[2:30:1]	Generators of the group modulo torsion
j	-192100033/44764	j-invariant
L	6.7800288053639	L(r)(E,1)/r!
Ω	1.7164692677306	Real period
R	1.9749927752357	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	1178d1 37696p1 84816n1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 9424d1

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	4	-6	-6	+	-6	-6	-	6	-6	12	0	2	-12	8	0	8	-10	-8	16	-8	-10

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Quadratic twists for elliptic curve 9424d1

-4	8	-3
1178d1	37696p1	84816n1

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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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