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	1340c	Isogeny class
Conductor	1340	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	84	Modular degree for the optimal curve
Δ	-5360 = -1 · 24 · 5 · 67	Discriminant
Eigenvalues	2-  1 5+  1 -6  2  4 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-6,5]	[a1,a2,a3,a4,a6]
Generators	[1:1:1]	Generators of the group modulo torsion
j	-1755904/335	j-invariant
L	2.8973229178286	L(r)(E,1)/r!
Ω	4.1205306296625	Real period
R	0.70314315757578	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5360i1 21440j1 12060d1 6700b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1340c1

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	+	1	-6	2	4	-8	4	-7	-4	-2	-4	-11	8	3	9	-12	-	12	14	-6	-16	1	-11

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Quadratic twists for elliptic curve 1340c1

-4	8	-3	5	-7	-67
5360i1	21440j1	12060d1	6700b1	65660h1	89780c1

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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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