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	36	Product of Tamagawa factors cp
Δ	-24291459037755 = -1 · 33 · 5 · 712 · 13	Discriminant
Eigenvalues	-1 3- 5+ 7- -4 13+  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,6909,86436]	[a1,a2,a3,a4,a6]
Generators	[0:294:1]	Generators of the group modulo torsion
j	36472485598112591/24291459037755	j-invariant
L	2.0017805909219	L(r)(E,1)/r!
Ω	0.42257691772304	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	21840ba3 87360bq3 4095m4 6825b4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1365d4

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 1365d4

-4	8	-3	5	-7	13
21840ba3	87360bq3	4095m4	6825b4	9555l4	17745s4

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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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