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	12992bc	Isogeny class
Conductor	12992	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	24576	Modular degree for the optimal curve
Δ	-15898862092288 = -1 · 216 · 73 · 294	Discriminant
Eigenvalues	2-  2  0 7+  0 -4  2  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-8513,-355231]	[a1,a2,a3,a4,a6]
Generators	[300475:8836416:343]	Generators of the group modulo torsion
j	-1041220466500/242597383	j-invariant
L	6.3523078135183	L(r)(E,1)/r!
Ω	0.24547706618522	Real period
R	6.4693495732972	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	12992t1 3248b1 116928dg1 90944eg1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12992bc1

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 12992bc1

-4	8	-3	-7
12992t1	3248b1	116928dg1	90944eg1

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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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