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	12432bw	Isogeny class
Conductor	12432	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	2349648 = 24 · 34 · 72 · 37	Discriminant
Eigenvalues	2- 3-  0 7-  0  4 -8 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-33,-18]	[a1,a2,a3,a4,a6]
Generators	[6:6:1]	Generators of the group modulo torsion
j	256000000/146853	j-invariant
L	5.8505731172804	L(r)(E,1)/r!
Ω	2.1568201972739	Real period
R	1.3562959779112	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	3108b1 49728dj1 37296ch1 87024ci1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12432bw1

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	4	-8	-8	6	2	8	-	2	-10	-8	-10	8	0	-12	-12	-6	10	12	-8	-16

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Quadratic twists for elliptic curve 12432bw1

-4	8	-3	-7
3108b1	49728dj1	37296ch1	87024ci1

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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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