Cremona's table of elliptic curves

410 = 2 · 5 · 41

Field	Data	Notes
Atkin-Lehner	2+ 5- 41-	Signs for the Atkin-Lehner involutions
Class	410a	Isogeny class
Conductor	410	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	65600 = 26 · 52 · 41	Discriminant
Eigenvalues	2+  0 5- -2 -6 -2  8 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-14,20]	[a1,a2,a3,a4,a6]
Generators	[1:2:1]	Generators of the group modulo torsion
j	315821241/65600	j-invariant
L	1.3868548095141	L(r)(E,1)/r!
Ω	3.2967108101876	Real period
R	0.42067833345539	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	3280l1 13120j1 3690q1 2050f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 410a1

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

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Quadratic twists for elliptic curve 410a1

-4	8	-3	5	-7	-11	13	17	41
3280l1	13120j1	3690q1	2050f1	20090a1	49610w1	69290o1	118490a1	16810a1

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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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