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	12992t	Isogeny class
Conductor	12992	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	12968631861248 = 217 · 76 · 292	Discriminant
Eigenvalues	2+ -2  0 7-  0 -4  2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-143073,20781439]	[a1,a2,a3,a4,a6]
Generators	[210:203:1]	Generators of the group modulo torsion
j	2471097448795250/98942809	j-invariant
L	2.9542162135466	L(r)(E,1)/r!
Ω	0.66547430247551	Real period
R	0.73987735828847	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	12992bc2 1624b2 116928bx2 90944by2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12992t2

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

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Quadratic twists for elliptic curve 12992t2

-4	8	-3	-7
12992bc2	1624b2	116928bx2	90944by2

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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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