Cremona's table of elliptic curves

1340 = 2² · 5 · 67

Field	Data	Notes
Atkin-Lehner	2- 5+ 67+	Signs for the Atkin-Lehner involutions
Class	1340a	Isogeny class
Conductor	1340	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	540	Modular degree for the optimal curve
Δ	-3350000 = -1 · 24 · 55 · 67	Discriminant
Eigenvalues	2-  1 5+  5  0  2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1206,15725]	[a1,a2,a3,a4,a6]
j	-12134048168704/209375	j-invariant
L	2.3046369291837	L(r)(E,1)/r!
Ω	2.3046369291837	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5360k1 21440n1 12060c1 6700d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1340a1

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	+	5	0	2	2	4	-6	9	0	4	2	1	0	-13	1	-4	+	8	12	-10	14	5	-3

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Quadratic twists for elliptic curve 1340a1

-4	8	-3	5	-7	-67
5360k1	21440n1	12060c1	6700d1	65660d1	89780d1

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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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