Cremona's table of elliptic curves

6578 = 2 · 11 · 13 · 23

Field	Data	Notes
Atkin-Lehner	2- 11+ 13+ 23+	Signs for the Atkin-Lehner involutions
Class	6578c	Isogeny class
Conductor	6578	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	1600	Modular degree for the optimal curve
Δ	-19365632 = -1 · 28 · 11 · 13 · 232	Discriminant
Eigenvalues	2-  0  0  0 11+ 13+  8 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-120,-517]	[a1,a2,a3,a4,a6]
j	-189613868625/19365632	j-invariant
L	2.8702060530008	L(r)(E,1)/r!
Ω	0.7175515132502	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	52624f1 59202p1 72358d1 85514e1	Quadratic twists by: -4 -3 -11 13

Hecke Eigenvalues for elliptic curve 6578c1

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

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Quadratic twists for elliptic curve 6578c1

-4	-3	-11	13
52624f1	59202p1	72358d1	85514e1

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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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