Cremona's table of elliptic curves

940 = 2² · 5 · 47

Field	Data	Notes
Atkin-Lehner	2- 5- 47+	Signs for the Atkin-Lehner involutions
Class	940d	Isogeny class
Conductor	940	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	72	Modular degree for the optimal curve
Δ	60160 = 28 · 5 · 47	Discriminant
Eigenvalues	2- -1 5-  1 -1 -5  2 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-20,40]	[a1,a2,a3,a4,a6]
Generators	[2:2:1]	Generators of the group modulo torsion
j	3631696/235	j-invariant
L	2.1758274460484	L(r)(E,1)/r!
Ω	3.4473780398472	Real period
R	0.21038476400505	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3760o1 15040a1 8460e1 4700c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 940d1

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	-1	-5	2	-5	-4	8	-7	-2	-10	2	+	-4	-12	13	-8	-12	11	-12	-1	-2	10

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Quadratic twists for elliptic curve 940d1

-4	8	-3	5	-7	-11	-47
3760o1	15040a1	8460e1	4700c1	46060c1	113740g1	44180b1

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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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