Cremona's table of elliptic curves

40 = 2³ · 5

Field	Data	Notes
Atkin-Lehner	2+ 5-	Signs for the Atkin-Lehner involutions
Class	40a	Isogeny class
Conductor	40	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-640000 = -1 · 210 · 54	Discriminant
Eigenvalues	2+  0 5- -4  4 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,13,-34]	[a1,a2,a3,a4,a6]
j	237276/625	j-invariant
L	0.74220623671119	L(r)(E,1)/r!
Ω	1.4844124734224	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	80a4 320b4 360e4 200c4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 40a4

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	-2	2	4	4	-2	-8	6	-6	-8	4	6	-4	-2	8	0	-6	0	-16	-6	-14

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Quadratic twists for elliptic curve 40a4

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53
80a4	320b4	360e4	200c4	1960b4	4840g4	6760g4	11560a4	14440h4	21160c3	33640h3	38440e3	54760c3	67240e3	73960b3	88360c3	112360c3

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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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