Cremona's table of elliptic curves

12642 = 2 · 3 · 7² · 43

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 43-	Signs for the Atkin-Lehner involutions
Class	12642bf	Isogeny class
Conductor	12642	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	5040	Modular degree for the optimal curve
Δ	-106546776 = -1 · 23 · 3 · 74 · 432	Discriminant
Eigenvalues	2- 3- -3 7+  3 -2  4  6	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-197,-1191]	[a1,a2,a3,a4,a6]
j	-352263793/44376	j-invariant
L	3.7961593371133	L(r)(E,1)/r!
Ω	0.63269322285222	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	101136z1 37926i1 12642bb1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 12642bf1

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	-2	4	6	4	-1	-1	2	2	-	-4	-7	-5	-8	4	4	-6	7	-1	-4	-5

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Quadratic twists for elliptic curve 12642bf1

-4	-3	-7
101136z1	37926i1	12642bb1

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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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