Cremona's table of elliptic curves

24768 = 2⁶ · 3² · 43

Field	Data	Notes
Atkin-Lehner	2- 3+ 43-	Signs for the Atkin-Lehner involutions
Class	24768bt	Isogeny class
Conductor	24768	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	36864	Modular degree for the optimal curve
Δ	-1246614257664 = -1 · 230 · 33 · 43	Discriminant
Eigenvalues	2- 3+  3  1 -3  1 -6 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-13356,-596528]	[a1,a2,a3,a4,a6]
Generators	[22780:217296:125]	Generators of the group modulo torsion
j	-37226247219/176128	j-invariant
L	6.6542457589087	L(r)(E,1)/r!
Ω	0.22198699779188	Real period
R	7.4939589087413	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	24768c1 6192j1 24768bv2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 24768bt1

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	-3	1	-6	-1	0	3	4	-2	0	-	3	0	0	-14	-4	6	2	-14	9	-18	5

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Quadratic twists for elliptic curve 24768bt1

-4	8	-3
24768c1	6192j1	24768bv2

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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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