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	20	Product of Tamagawa factors cp
Δ	745537500000 = 25 · 33 · 58 · 472	Discriminant
Eigenvalues	2- 3+ 5+  0 -2 -4  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-3996,-89571]	[a1,a2,a3,a4,a6]
Generators	[-39:113:1]	Generators of the group modulo torsion
j	7056785934088129/745537500000	j-invariant
L	3.1935077245366	L(r)(E,1)/r!
Ω	0.60457574954987	Real period
R	1.0564458554331	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	11280r2 45120bm2 4230k2 7050e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1410j2

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 1410j2

-4	8	-3	5	-7	-47
11280r2	45120bm2	4230k2	7050e2	69090bw2	66270q2

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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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