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	2	Product of Tamagawa factors cp
Δ	5120 = 210 · 5	Discriminant
Eigenvalues	2+  0 5- -4  4 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-107,-426]	[a1,a2,a3,a4,a6]
j	132304644/5	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	2	Number of elements in the torsion subgroup
Twists	80a3 320b3 360e3 200c3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 40a2

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 40a2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53
80a3	320b3	360e3	200c3	1960b3	4840g3	6760g3	11560a3	14440h3	21160c4	33640h4	38440e4	54760c4	67240e4	73960b4	88360c4	112360c4

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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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