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	12432be	Isogeny class
Conductor	12432	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-40029647616 = -1 · 28 · 32 · 73 · 373	Discriminant
Eigenvalues	2- 3+ -3 7+ -3 -1 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,643,7089]	[a1,a2,a3,a4,a6]
Generators	[29:-222:1]	Generators of the group modulo torsion
j	114667692032/156365811	j-invariant
L	2.3719002419384	L(r)(E,1)/r!
Ω	0.77495667467981	Real period
R	0.25505729539852	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	3108j2 49728eb2 37296ca2 87024ej2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12432be2

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
-	+	-3	+	-3	-1	-6	4	-6	0	7	-	6	10	0	3	3	-10	7	-3	-4	-2	12	-3	5

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Quadratic twists for elliptic curve 12432be2

-4	8	-3	-7
3108j2	49728eb2	37296ca2	87024ej2

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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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