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	12432j	Isogeny class
Conductor	12432	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-3219888 = -1 · 24 · 3 · 72 · 372	Discriminant
Eigenvalues	2+ 3-  0 7+  0 -2  4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,37,0]	[a1,a2,a3,a4,a6]
Generators	[36:222:1]	Generators of the group modulo torsion
j	340736000/201243	j-invariant
L	5.4222452147418	L(r)(E,1)/r!
Ω	1.4764775851493	Real period
R	3.6724195946352	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	6216e1 49728cq1 37296m1 87024m1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12432j1

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
+	-	0	+	0	-2	4	-4	2	-4	4	-	-6	4	8	2	-6	-6	4	-8	14	-4	-16	0	-6

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Quadratic twists for elliptic curve 12432j1

-4	8	-3	-7
6216e1	49728cq1	37296m1	87024m1

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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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