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	12	Product of Tamagawa factors cp
Δ	-1849600 = -1 · 28 · 52 · 172	Discriminant
Eigenvalues	2-  0 5+ -4  2 -6 17-  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-23,78]	[a1,a2,a3,a4,a6]
Generators	[-1:10:1]	Generators of the group modulo torsion
j	-5256144/7225	j-invariant
L	1.5553431744493	L(r)(E,1)/r!
Ω	2.3774597281075	Real period
R	0.21806793136687	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	1360e2 5440i2 3060l2 1700a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 340a2

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 340a2

-4	8	-3	5	-7	-11	13	17	-19
1360e2	5440i2	3060l2	1700a2	16660h2	41140a2	57460d2	5780d2	122740g2

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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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