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	12432d	Isogeny class
Conductor	12432	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-204475767552 = -1 · 28 · 35 · 74 · 372	Discriminant
Eigenvalues	2+ 3+  0 7+  4  2 -4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,692,20368]	[a1,a2,a3,a4,a6]
j	142946750000/798733467	j-invariant
L	1.4471839612765	L(r)(E,1)/r!
Ω	0.72359198063825	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6216u2 49728dz2 37296o2 87024bi2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12432d2

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	+	4	2	-4	-4	6	-4	-4	-	6	0	0	-14	6	6	12	4	6	16	0	-16	14

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Quadratic twists for elliptic curve 12432d2

-4	8	-3	-7
6216u2	49728dz2	37296o2	87024bi2

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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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