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	4	Product of Tamagawa factors cp
deg	2	Modular degree for the optimal curve
Δ	6400 = 28 · 52	Discriminant
Eigenvalues	2+  0 5- -4  4 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-7,-6]	[a1,a2,a3,a4,a6]
j	148176/25	j-invariant
L	0.74220623671119	L(r)(E,1)/r!
Ω	2.9688249468448	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	80a1 320b2 360e2 200c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 40a1

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 40a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53
80a1	320b2	360e2	200c2	1960b2	4840g2	6760g2	11560a2	14440h2	21160c2	33640h2	38440e2	54760c2	67240e2	73960b2	88360c2	112360c2

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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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