Cremona's table of elliptic curves

118976 = 2⁶ · 11 · 13²

Field	Data	Notes
Atkin-Lehner	2- 11- 13+	Signs for the Atkin-Lehner involutions
Class	118976cz	Isogeny class
Conductor	118976	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	774144	Modular degree for the optimal curve
Δ	-15922774528753664 = -1 · 221 · 112 · 137	Discriminant
Eigenvalues	2- -1 -1  1 11- 13+ -1  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-362561,-84125471]	[a1,a2,a3,a4,a6]
Generators	[23877:3688256:1]	Generators of the group modulo torsion
j	-4165509529/12584	j-invariant
L	5.8076152671964	L(r)(E,1)/r!
Ω	0.09726254238899	Real period
R	3.7319192286446	Regulator
r	1	Rank of the group of rational points
S	1.0000000055966	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	118976d1 29744l1 9152u1	Quadratic twists by: -4 8 13

Hecke Eigenvalues for elliptic curve 118976cz1

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	-1	1	-	+	-1	4	8	8	0	7	8	11	-1	-2	-14	8	-8	9	4	-2	0	4	-8

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Quadratic twists for elliptic curve 118976cz1

-4	8	13
118976d1	29744l1	9152u1

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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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