Cremona's table of elliptic curves

4851 = 3² · 7² · 11

Field	Data	Notes
Atkin-Lehner	3+ 7- 11-	Signs for the Atkin-Lehner involutions
Class	4851f	Isogeny class
Conductor	4851	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	4320	Modular degree for the optimal curve
Δ	25472537937 = 39 · 76 · 11	Discriminant
Eigenvalues	1 3+ -4 7- 11-  2  2  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-744,-1261]	[a1,a2,a3,a4,a6]
Generators	[-22:75:1]	Generators of the group modulo torsion
j	19683/11	j-invariant
L	3.488010977087	L(r)(E,1)/r!
Ω	0.9816428982373	Real period
R	3.5532381310457	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	77616do1 4851d1 121275bg1 99c1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4851f1

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	+	-4	-	-	2	2	6	-4	6	-4	-6	-10	6	-8	0	4	6	8	0	2	-10	12	0	-2

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Quadratic twists for elliptic curve 4851f1

-4	-3	5	-7	-11
77616do1	4851d1	121275bg1	99c1	53361n1

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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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