Cremona's table of elliptic curves

4128 = 2⁵ · 3 · 43

Field	Data	Notes
Atkin-Lehner	2+ 3- 43-	Signs for the Atkin-Lehner involutions
Class	4128f	Isogeny class
Conductor	4128	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-4755456 = -1 · 212 · 33 · 43	Discriminant
Eigenvalues	2+ 3-  1  1 -5 -5  2  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-65,207]	[a1,a2,a3,a4,a6]
Generators	[7:-12:1]	Generators of the group modulo torsion
j	-7529536/1161	j-invariant
L	4.4344230572364	L(r)(E,1)/r!
Ω	2.3538599770661	Real period
R	0.1569911797516	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	4128i1 8256d1 12384p1 103200bn1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4128f1

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
+	-	1	1	-5	-5	2	1	-8	9	4	0	-8	-	-9	0	4	4	-14	-14	-6	8	-5	6	-7

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Quadratic twists for elliptic curve 4128f1

-4	8	-3	5
4128i1	8256d1	12384p1	103200bn1

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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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