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	12432t	Isogeny class
Conductor	12432	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	5569536 = 210 · 3 · 72 · 37	Discriminant
Eigenvalues	2+ 3-  2 7-  4 -2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-116032,-15251740]	[a1,a2,a3,a4,a6]
j	168717772351634692/5439	j-invariant
L	4.1388032448829	L(r)(E,1)/r!
Ω	0.25867520280518	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	16	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6216m4 49728do4 37296bf4 87024t4	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12432t3

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

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Quadratic twists for elliptic curve 12432t3

-4	8	-3	-7
6216m4	49728do4	37296bf4	87024t4

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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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