Cremona's table of elliptic curves

440 = 2³ · 5 · 11

Field	Data	Notes
Atkin-Lehner	2+ 5+ 11+	Signs for the Atkin-Lehner involutions
Class	440a	Isogeny class
Conductor	440	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	242000 = 24 · 53 · 112	Discriminant
Eigenvalues	2+  0 5+ -2 11+  0  0 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-38,-87]	[a1,a2,a3,a4,a6]
Generators	[-4:1:1]	Generators of the group modulo torsion
j	379275264/15125	j-invariant
L	1.7340332812889	L(r)(E,1)/r!
Ω	1.9276140142219	Real period
R	0.89957495042847	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	880b1 3520l1 3960s1 2200e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 440a1

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	+	0	0	-8	-8	10	8	-10	-2	-6	-8	14	-4	10	4	0	-8	-4	10	6	-10

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Quadratic twists for elliptic curve 440a1

-4	8	-3	5	-7	-11	13	17
880b1	3520l1	3960s1	2200e1	21560i1	4840f1	74360s1	127160g1

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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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