Cremona's table of elliptic curves

6432 = 2⁵ · 3 · 67

Field	Data	Notes
Atkin-Lehner	2- 3+ 67-	Signs for the Atkin-Lehner involutions
Class	6432m	Isogeny class
Conductor	6432	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	172800	Modular degree for the optimal curve
Δ	4677466176 = 26 · 35 · 673	Discriminant
Eigenvalues	2- 3+  2 -2 -4  4  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-24361802,46290133200]	[a1,a2,a3,a4,a6]
Generators	[3801369:741690:1331]	Generators of the group modulo torsion
j	24984575986936074490505152/73085409	j-invariant
L	3.6936667394153	L(r)(E,1)/r!
Ω	0.43665163703485	Real period
R	5.6393799635451	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6432e1 12864n1 19296h1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 6432m1

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
-	+	2	-2	-4	4	6	4	-6	-4	-10	-2	2	-4	10	-14	4	12	-	10	-6	2	0	-14	-2

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Quadratic twists for elliptic curve 6432m1

-4	8	-3
6432e1	12864n1	19296h1

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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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