Cremona's table of elliptic curves

1365 = 3 · 5 · 7 · 13

Field	Data	Notes
Atkin-Lehner	3- 5+ 7- 13+	Signs for the Atkin-Lehner involutions
Class	1365d	Isogeny class
Conductor	1365	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	864	Modular degree for the optimal curve
Δ	1322517105 = 33 · 5 · 73 · 134	Discriminant
Eigenvalues	-1 3- 5+ 7- -4 13+  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1021,-12520]	[a1,a2,a3,a4,a6]
Generators	[-19:20:1]	Generators of the group modulo torsion
j	117713838907729/1322517105	j-invariant
L	2.0017805909219	L(r)(E,1)/r!
Ω	0.84515383544608	Real period
R	0.52634220263722	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	21840ba1 87360bq1 4095m1 6825b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1365d1

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	-	+	-	-4	+	2	0	0	-10	-4	10	6	-8	4	-10	-12	-10	-4	0	6	0	-16	-10	-2

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Quadratic twists for elliptic curve 1365d1

-4	8	-3	5	-7	13
21840ba1	87360bq1	4095m1	6825b1	9555l1	17745s1

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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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