Cremona's table of elliptic curves

340 = 2² · 5 · 17

Field	Data	Notes
Atkin-Lehner	2- 5+ 17-	Signs for the Atkin-Lehner involutions
Class	340a	Isogeny class
Conductor	340	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	24	Modular degree for the optimal curve
Δ	1360 = 24 · 5 · 17	Discriminant
Eigenvalues	2-  0 5+ -4  2 -6 17-  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-28,57]	[a1,a2,a3,a4,a6]
Generators	[2:3:1]	Generators of the group modulo torsion
j	151732224/85	j-invariant
L	1.5553431744493	L(r)(E,1)/r!
Ω	4.754919456215	Real period
R	0.43613586273374	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	1360e1 5440i1 3060l1 1700a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 340a1

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	+	-4	2	-6	-	0	0	-6	6	-2	-6	6	-10	-6	0	10	-2	6	6	6	6	-18	-14

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Quadratic twists for elliptic curve 340a1

-4	8	-3	5	-7	-11	13	17	-19
1360e1	5440i1	3060l1	1700a1	16660h1	41140a1	57460d1	5780d1	122740g1

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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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