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	12432bp	Isogeny class
Conductor	12432	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	3456	Modular degree for the optimal curve
Δ	-25460736 = -1 · 215 · 3 · 7 · 37	Discriminant
Eigenvalues	2- 3- -3 7+ -2 -4  4  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-112,-556]	[a1,a2,a3,a4,a6]
Generators	[28:138:1]	Generators of the group modulo torsion
j	-38272753/6216	j-invariant
L	4.143842142788	L(r)(E,1)/r!
Ω	0.72675565408011	Real period
R	2.8509184067051	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	1554j1 49728dg1 37296br1 87024cd1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12432bp1

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	+	-2	-4	4	5	2	-6	0	+	-5	8	2	9	10	-8	15	3	-10	-8	5	16	-15

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Quadratic twists for elliptic curve 12432bp1

-4	8	-3	-7
1554j1	49728dg1	37296br1	87024cd1

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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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