Cremona's table of elliptic curves

12432 = 2⁴ · 3 · 7 · 37

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 37-	Signs for the Atkin-Lehner involutions
Class	12432bk	Isogeny class
Conductor	12432	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	-4478837212459008 = -1 · 212 · 35 · 74 · 374	Discriminant
Eigenvalues	2- 3+ -2 7-  0 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1624,3220528]	[a1,a2,a3,a4,a6]
j	-115714886617/1093466116323	j-invariant
L	1.3952396560559	L(r)(E,1)/r!
Ω	0.34880991401397	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	777e4 49728eq3 37296cm3 87024eg3	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12432bk4

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	-2	2	4	8	-6	8	-	6	4	-8	6	0	-2	-12	12	2	-16	-12	10	-14

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Quadratic twists for elliptic curve 12432bk4

-4	8	-3	-7
777e4	49728eq3	37296cm3	87024eg3

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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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