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	410d	Isogeny class
Conductor	410	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	64	Modular degree for the optimal curve
Δ	262400 = 28 · 52 · 41	Discriminant
Eigenvalues	2- -2 5+ -2  2 -6 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-16,0]	[a1,a2,a3,a4,a6]
Generators	[-2:6:1]	Generators of the group modulo torsion
j	454756609/262400	j-invariant
L	1.8491499415013	L(r)(E,1)/r!
Ω	2.6404517310508	Real period
R	0.17507893817523	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	3280h1 13120s1 3690j1 2050c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 410d1

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
-	-2	+	-2	2	-6	-6	-2	-4	-6	0	10	-	4	2	-6	12	-10	2	10	-10	-6	0	10	2

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Quadratic twists for elliptic curve 410d1

-4	8	-3	5	-7	-11	13	17	41
3280h1	13120s1	3690j1	2050c1	20090j1	49610b1	69290k1	118490s1	16810e1

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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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