Cremona's table of elliptic curves

5978 = 2 · 7² · 61

Field	Data	Notes
Atkin-Lehner	2+ 7- 61+	Signs for the Atkin-Lehner involutions
Class	5978c	Isogeny class
Conductor	5978	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	512	Modular degree for the optimal curve
Δ	83692 = 22 · 73 · 61	Discriminant
Eigenvalues	2+ -1 -2 7- -3  2 -5 -5	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-11,1]	[a1,a2,a3,a4,a6]
Generators	[-4:3:1] [-1:4:1]	Generators of the group modulo torsion
j	493039/244	j-invariant
L	3.0702027270191	L(r)(E,1)/r!
Ω	3.0284093149394	Real period
R	0.25345011256175	Regulator
r	2	Rank of the group of rational points
S	1.0000000000004	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	47824j1 53802bx1 5978d1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 5978c1

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	-2	-	-3	2	-5	-5	-7	0	0	-4	-8	-5	3	-2	-8	+	-13	-7	-4	13	15	-9	8

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Quadratic twists for elliptic curve 5978c1

-4	-3	-7
47824j1	53802bx1	5978d1

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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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