Cremona's table of elliptic curves

1410 = 2 · 3 · 5 · 47

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 47-	Signs for the Atkin-Lehner involutions
Class	1410j	Isogeny class
Conductor	1410	Conductor
∏ cp	40	Product of Tamagawa factors cp
deg	960	Modular degree for the optimal curve
Δ	-21928320000 = -1 · 210 · 36 · 54 · 47	Discriminant
Eigenvalues	2- 3+ 5+  0 -2 -4  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,324,-6627]	[a1,a2,a3,a4,a6]
Generators	[21:89:1]	Generators of the group modulo torsion
j	3760754329151/21928320000	j-invariant
L	3.1935077245366	L(r)(E,1)/r!
Ω	0.60457574954987	Real period
R	0.52822292771655	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	11280r1 45120bm1 4230k1 7050e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1410j1

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

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Quadratic twists for elliptic curve 1410j1

-4	8	-3	5	-7	-47
11280r1	45120bm1	4230k1	7050e1	69090bw1	66270q1

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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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