Cremona's table of elliptic curves

129472 = 2⁶ · 7 · 17²

Field	Data	Notes
Atkin-Lehner	2+ 7+ 17+	Signs for the Atkin-Lehner involutions
Class	129472f	Isogeny class
Conductor	129472	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	705024	Modular degree for the optimal curve
Δ	903165267401152 = 26 · 7 · 1710	Discriminant
Eigenvalues	2+  1 -4 7+  2  4 17+  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-27840,-1061026]	[a1,a2,a3,a4,a6]
Generators	[-28674662:275064017:551368]	Generators of the group modulo torsion
j	18496/7	j-invariant
L	5.2878238201021	L(r)(E,1)/r!
Ω	0.38152526852487	Real period
R	13.859694645268	Regulator
r	1	Rank of the group of rational points
S	1.0000000187021	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	129472bd1 64736m1 129472bp1	Quadratic twists by: -4 8 17

Hecke Eigenvalues for elliptic curve 129472f1

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	-4	+	2	4	+	1	-2	-9	7	-6	10	-4	-7	-9	7	8	12	0	0	14	-17	-8	12

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Quadratic twists for elliptic curve 129472f1

-4	8	17
129472bd1	64736m1	129472bp1

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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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