Cremona's table of elliptic curves

3096 = 2³ · 3² · 43

Field	Data	Notes
Atkin-Lehner	2+ 3- 43-	Signs for the Atkin-Lehner involutions
Class	3096d	Isogeny class
Conductor	3096	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	512	Modular degree for the optimal curve
Δ	-8024832 = -1 · 28 · 36 · 43	Discriminant
Eigenvalues	2+ 3-  2 -2 -1 -1  7 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,36,-108]	[a1,a2,a3,a4,a6]
Generators	[6:18:1]	Generators of the group modulo torsion
j	27648/43	j-invariant
L	3.5926221197195	L(r)(E,1)/r!
Ω	1.2333090298779	Real period
R	0.36412428198096	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	6192e1 24768r1 344a1 77400be1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3096d1

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	-1	-1	7	-6	-9	-4	1	-4	11	-	0	-11	-12	0	7	10	-4	-8	3	-6	3

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Quadratic twists for elliptic curve 3096d1

-4	8	-3	5
6192e1	24768r1	344a1	77400be1

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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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