Cremona's table of elliptic curves

42432 = 2⁶ · 3 · 13 · 17

Field	Data	Notes
Atkin-Lehner	2- 3+ 13+ 17-	Signs for the Atkin-Lehner involutions
Class	42432bk	Isogeny class
Conductor	42432	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1527367335936 = 220 · 3 · 134 · 17	Discriminant
Eigenvalues	2- 3+  2  0  0 13+ 17-  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-69857,-7083135]	[a1,a2,a3,a4,a6]
Generators	[25226:1411165:8]	Generators of the group modulo torsion
j	143820170742457/5826444	j-invariant
L	5.5734921817057	L(r)(E,1)/r!
Ω	0.29366190349847	Real period
R	9.4896411746104	Regulator
r	1	Rank of the group of rational points
S	0.99999999999974	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	42432r4 10608z3 127296cd4	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 42432bk4

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	0	0	+	-	0	0	2	-8	-10	-6	-4	8	2	-4	10	8	12	6	8	12	-10	6

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Quadratic twists for elliptic curve 42432bk4

-4	8	-3
42432r4	10608z3	127296cd4

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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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