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	12864c	Isogeny class
Conductor	12864	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-8719428929716224 = -1 · 230 · 33 · 673	Discriminant
Eigenvalues	2+ 3+  3 -1  0  4 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,51231,496737]	[a1,a2,a3,a4,a6]
Generators	[7369:632832:1]	Generators of the group modulo torsion
j	56724909592967/33261981696	j-invariant
L	4.7600001055242	L(r)(E,1)/r!
Ω	0.24997611187958	Real period
R	4.7604549788115	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	12864bn2 402d2 38592r2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 12864c2

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
+	+	3	-1	0	4	-6	-2	-9	0	5	7	3	1	0	-9	3	10	+	-12	11	8	-15	0	8

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Quadratic twists for elliptic curve 12864c2

-4	8	-3
12864bn2	402d2	38592r2

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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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