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	4	Product of Tamagawa factors cp
Δ	110012474 = 2 · 114 · 13 · 172	Discriminant
Eigenvalues	2+ -2 -2 -2 11+ 13- 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-182,-810]	[a1,a2,a3,a4,a6]
Generators	[-10:10:1] [-6:11:1]	Generators of the group modulo torsion
j	661459323097/110012474	j-invariant
L	2.4684117134919	L(r)(E,1)/r!
Ω	1.3153684204242	Real period
R	1.8765934130424	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	38896k2 43758z2 121550bk2 53482n2	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4862a2

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 4862a2

-4	-3	5	-11	13	17
38896k2	43758z2	121550bk2	53482n2	63206l2	82654h2

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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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