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	4851j	Isogeny class
Conductor	4851	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	3456	Modular degree for the optimal curve
Δ	25472537937 = 39 · 76 · 11	Discriminant
Eigenvalues	-1 3- -2 7- 11+  2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-2876,-58138]	[a1,a2,a3,a4,a6]
Generators	[-32:34:1]	Generators of the group modulo torsion
j	30664297/297	j-invariant
L	1.9825722734783	L(r)(E,1)/r!
Ω	0.65233108844474	Real period
R	3.0392116957127	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	77616gn1 1617j1 121275de1 99b1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4851j1

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	-	-2	-	+	2	-2	0	-8	6	8	6	-2	0	8	-6	-4	-6	-4	0	14	-4	12	-6	-2

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Quadratic twists for elliptic curve 4851j1

-4	-3	5	-7	-11
77616gn1	1617j1	121275de1	99b1	53361bj1

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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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