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	12432s	Isogeny class
Conductor	12432	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	6912	Modular degree for the optimal curve
Δ	202852944 = 24 · 33 · 73 · 372	Discriminant
Eigenvalues	2+ 3- -2 7- -4  0  2  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-3099,65376]	[a1,a2,a3,a4,a6]
Generators	[36:42:1]	Generators of the group modulo torsion
j	205782571927552/12678309	j-invariant
L	4.9186833558404	L(r)(E,1)/r!
Ω	1.6907324611476	Real period
R	0.64648947770271	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	6216d1 49728du1 37296z1 87024j1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12432s1

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	0	2	2	6	-4	-2	+	10	-8	0	-6	0	-8	-12	8	10	12	-12	6	-8

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Quadratic twists for elliptic curve 12432s1

-4	8	-3	-7
6216d1	49728du1	37296z1	87024j1

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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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