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	12432bx	Isogeny class
Conductor	12432	Conductor
∏ cp	130	Product of Tamagawa factors cp
deg	873600	Modular degree for the optimal curve
Δ	-8.6705917744885E+20	Discriminant
Eigenvalues	2- 3-  1 7- -1 -1  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-40511205,-99269123373]	[a1,a2,a3,a4,a6]
Generators	[22302:3176523:1]	Generators of the group modulo torsion
j	-1795102530323910983888896/211684369494348891	j-invariant
L	6.1111070035412	L(r)(E,1)/r!
Ω	0.029920765139378	Real period
R	1.5711000434942	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	777b1 49728dk1 37296ci1 87024co1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12432bx1

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	-	-1	-1	2	-4	-6	-8	9	-	6	-2	-12	11	5	-2	-15	-5	-8	-10	0	13	9

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Quadratic twists for elliptic curve 12432bx1

-4	8	-3	-7
777b1	49728dk1	37296ci1	87024co1

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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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