Cremona's table of elliptic curves

12992 = 2⁶ · 7 · 29

Field	Data	Notes
Atkin-Lehner	2+ 7- 29+	Signs for the Atkin-Lehner involutions
Class	12992m	Isogeny class
Conductor	12992	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	4096	Modular degree for the optimal curve
Δ	-372506624 = -1 · 218 · 72 · 29	Discriminant
Eigenvalues	2+  1 -1 7-  5  5 -4  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1,-929]	[a1,a2,a3,a4,a6]
j	-1/1421	j-invariant
L	3.1057283121557	L(r)(E,1)/r!
Ω	0.77643207803891	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	12992y1 203b1 116928ch1 90944v1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12992m1

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	-	5	5	-4	4	6	+	7	10	0	9	7	-3	0	-14	6	8	-16	-9	-16	-6	0

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Quadratic twists for elliptic curve 12992m1

-4	8	-3	-7
12992y1	203b1	116928ch1	90944v1

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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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