Cremona's table of elliptic curves

4862 = 2 · 11 · 13 · 17

Field	Data	Notes
Atkin-Lehner	2+ 11+ 13- 17+	Signs for the Atkin-Lehner involutions
Class	4862a	Isogeny class
Conductor	4862	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	896	Modular degree for the optimal curve
Δ	1390532 = 22 · 112 · 132 · 17	Discriminant
Eigenvalues	2+ -2 -2 -2 11+ 13- 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-52,126]	[a1,a2,a3,a4,a6]
Generators	[-8:10:1] [-4:18:1]	Generators of the group modulo torsion
j	15124197817/1390532	j-invariant
L	2.4684117134919	L(r)(E,1)/r!
Ω	2.6307368408484	Real period
R	0.46914835326061	Regulator
r	2	Rank of the group of rational points
S	0.99999999999994	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	38896k1 43758z1 121550bk1 53482n1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4862a1

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

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Quadratic twists for elliptic curve 4862a1

-4	-3	5	-11	13	17
38896k1	43758z1	121550bk1	53482n1	63206l1	82654h1

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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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