Cremona's table of elliptic curves

5369 = 7 · 13 · 59

Field	Data	Notes
Atkin-Lehner	7+ 13- 59+	Signs for the Atkin-Lehner involutions
Class	5369b	Isogeny class
Conductor	5369	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	2016	Modular degree for the optimal curve
Δ	-53534299 = -1 · 7 · 133 · 592	Discriminant
Eigenvalues	-2 -2 -1 7+ -2 13-  0 -5	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-96,474]	[a1,a2,a3,a4,a6]
Generators	[-12:6:1] [-6:29:1]	Generators of the group modulo torsion
j	-98867482624/53534299	j-invariant
L	1.9198072593571	L(r)(E,1)/r!
Ω	1.8523128658218	Real period
R	0.17273965023055	Regulator
r	2	Rank of the group of rational points
S	0.99999999999969	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	85904bc1 48321m1 37583d1 69797c1	Quadratic twists by: -4 -3 -7 13

Hecke Eigenvalues for elliptic curve 5369b1

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
-2	-2	-1	+	-2	-	0	-5	-7	-1	-3	2	-2	1	-9	-13	+	6	4	8	-13	-1	7	-9	-17

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Quadratic twists for elliptic curve 5369b1

-4	-3	-7	13
85904bc1	48321m1	37583d1	69797c1

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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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