Cremona's table of elliptic curves

12864 = 2⁶ · 3 · 67

Field	Data	Notes
Atkin-Lehner	2+ 3+ 67+	Signs for the Atkin-Lehner involutions
Class	12864b	Isogeny class
Conductor	12864	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1920	Modular degree for the optimal curve
Δ	-3125952 = -1 · 26 · 36 · 67	Discriminant
Eigenvalues	2+ 3+  2  2  0  4 -7 -7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-7,-83]	[a1,a2,a3,a4,a6]
Generators	[74:189:8]	Generators of the group modulo torsion
j	-681472/48843	j-invariant
L	4.9470005139498	L(r)(E,1)/r!
Ω	1.1130273204268	Real period
R	2.2223176480757	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	12864t1 6432i1 38592q1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 12864b1

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	2	0	4	-7	-7	3	-1	8	1	-10	8	-7	0	-3	-10	+	0	-7	6	0	-7	-6

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Quadratic twists for elliptic curve 12864b1

-4	8	-3
12864t1	6432i1	38592q1

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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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