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	12432bj	Isogeny class
Conductor	12432	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	8064	Modular degree for the optimal curve
Δ	-4640219136 = -1 · 213 · 37 · 7 · 37	Discriminant
Eigenvalues	2- 3+  1 7-  6  4 -4  5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,280,-2832]	[a1,a2,a3,a4,a6]
j	590589719/1132866	j-invariant
L	2.8719287421444	L(r)(E,1)/r!
Ω	0.7179821855361	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1554b1 49728eo1 37296cl1 87024ee1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12432bj1

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	-	6	4	-4	5	6	6	0	-	-7	8	2	5	14	4	7	-9	2	-16	7	-8	17

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Quadratic twists for elliptic curve 12432bj1

-4	8	-3	-7
1554b1	49728eo1	37296cl1	87024ee1

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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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