Cremona's table of elliptic curves

4340 = 2² · 5 · 7 · 31

Field	Data	Notes
Atkin-Lehner	2- 5- 7- 31-	Signs for the Atkin-Lehner involutions
Class	4340a	Isogeny class
Conductor	4340	Conductor
∏ cp	54	Product of Tamagawa factors cp
deg	1728	Modular degree for the optimal curve
Δ	-10547936000 = -1 · 28 · 53 · 73 · 312	Discriminant
Eigenvalues	2-  1 5- 7- -3 -1 -3  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-285,5183]	[a1,a2,a3,a4,a6]
Generators	[13:62:1]	Generators of the group modulo torsion
j	-10035552256/41202875	j-invariant
L	4.4423647167406	L(r)(E,1)/r!
Ω	1.1188109659084	Real period
R	0.66176873664768	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	17360bc1 69440r1 39060d1 21700b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4340a1

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
-	1	-	-	-3	-1	-3	2	0	-3	-	2	0	-10	3	6	-6	-10	-4	-12	-10	-1	12	0	-13

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Quadratic twists for elliptic curve 4340a1

-4	8	-3	5	-7
17360bc1	69440r1	39060d1	21700b1	30380a1

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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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