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	4851b	Isogeny class
Conductor	4851	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	9408	Modular degree for the optimal curve
Δ	-2278866188907 = -1 · 33 · 78 · 114	Discriminant
Eigenvalues	0 3+  4 7+ 11-  5  4 -3	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-2058,-81034]	[a1,a2,a3,a4,a6]
j	-6193152/14641	j-invariant
L	2.6468900514817	L(r)(E,1)/r!
Ω	0.33086125643522	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	77616cw1 4851a1 121275h1 4851e1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4851b1

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
0	+	4	+	-	5	4	-3	8	-4	1	7	-4	1	-8	-12	0	-2	3	-4	-11	15	12	12	-2

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Quadratic twists for elliptic curve 4851b1

-4	-3	5	-7	-11
77616cw1	4851a1	121275h1	4851e1	53361d1

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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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