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	5978a	Isogeny class
Conductor	5978	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	60840	Modular degree for the optimal curve
Δ	-80517786257850368 = -1 · 239 · 74 · 61	Discriminant
Eigenvalues	2+ -1 -2 7+  4  2  2 -5	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-182501,-33044339]	[a1,a2,a3,a4,a6]
Generators	[1245:40261:1]	Generators of the group modulo torsion
j	-279982582954788217/33535104647168	j-invariant
L	2.0697194477403	L(r)(E,1)/r!
Ω	0.11472147027061	Real period
R	6.0137520984755	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	47824c1 53802bs1 5978e1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 5978a1

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	+	4	2	2	-5	0	-7	7	-11	6	2	10	-9	-8	+	-6	0	17	13	1	-2	1

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Quadratic twists for elliptic curve 5978a1

-4	-3	-7
47824c1	53802bs1	5978e1

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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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