Cremona's table of elliptic curves

10440 = 2³ · 3² · 5 · 29

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 29-	Signs for the Atkin-Lehner involutions
Class	10440f	Isogeny class
Conductor	10440	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	974177280 = 210 · 38 · 5 · 29	Discriminant
Eigenvalues	2+ 3- 5+  0  0 -4  2  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-363,2198]	[a1,a2,a3,a4,a6]
Generators	[-2:54:1]	Generators of the group modulo torsion
j	7086244/1305	j-invariant
L	4.1509578943039	L(r)(E,1)/r!
Ω	1.4884174649493	Real period
R	1.3944199097547	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	20880n1 83520bw1 3480p1 52200bv1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10440f1

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	0	-4	2	6	2	-	-4	-2	0	-8	-8	6	-4	8	-6	0	-10	4	0	16	2

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Quadratic twists for elliptic curve 10440f1

-4	8	-3	5
20880n1	83520bw1	3480p1	52200bv1

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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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