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	12432w	Isogeny class
Conductor	12432	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	7680	Modular degree for the optimal curve
Δ	-5652283392 = -1 · 216 · 32 · 7 · 372	Discriminant
Eigenvalues	2- 3+  0 7+ -4 -4  0 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-768,9216]	[a1,a2,a3,a4,a6]
Generators	[-30:66:1] [0:96:1]	Generators of the group modulo torsion
j	-12246522625/1379952	j-invariant
L	5.4241625555489	L(r)(E,1)/r!
Ω	1.31499403377	Real period
R	1.0312142899994	Regulator
r	2	Rank of the group of rational points
S	0.99999999999982	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1554l1 49728ee1 37296bl1 87024dk1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12432w1

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	+	-4	-4	0	-6	-4	-10	-10	+	2	0	-4	-6	-6	8	4	8	-14	8	-12	0	-8

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Quadratic twists for elliptic curve 12432w1

-4	8	-3	-7
1554l1	49728ee1	37296bl1	87024dk1

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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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