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	12992f	Isogeny class
Conductor	12992	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	28620428935168 = 223 · 76 · 29	Discriminant
Eigenvalues	2+  0  0 7+  4  0 -4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-316300,68468976]	[a1,a2,a3,a4,a6]
j	13350003080765625/109178272	j-invariant
L	1.1932917061589	L(r)(E,1)/r!
Ω	0.59664585307947	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	12992bi2 406a2 116928x2 90944bj2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12992f2

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	0	+	4	0	-4	-4	0	-	-6	2	-8	-4	2	2	10	2	-8	16	0	-4	6	0	12

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Quadratic twists for elliptic curve 12992f2

-4	8	-3	-7
12992bi2	406a2	116928x2	90944bj2

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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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