Cremona's table of elliptic curves

492 = 2² · 3 · 41

Field	Data	Notes
Atkin-Lehner	2- 3- 41+	Signs for the Atkin-Lehner involutions
Class	492b	Isogeny class
Conductor	492	Conductor
∏ cp	27	Product of Tamagawa factors cp
deg	216	Modular degree for the optimal curve
Δ	-206592768 = -1 · 28 · 39 · 41	Discriminant
Eigenvalues	2- 3- -2 -4 -5  4 -5 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,11,695]	[a1,a2,a3,a4,a6]
Generators	[-7:18:1]	Generators of the group modulo torsion
j	524288/807003	j-invariant
L	1.9348232248738	L(r)(E,1)/r!
Ω	1.3947922132698	Real period
R	0.051376913892985	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1968f1 7872c1 1476b1 12300a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 492b1

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	-4	-5	4	-5	-6	4	-3	1	5	+	9	-11	2	-4	1	-14	-1	13	10	-6	-14	-6

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Quadratic twists for elliptic curve 492b1

-4	8	-3	5	-7	-11	13	41
1968f1	7872c1	1476b1	12300a1	24108c1	59532j1	83148l1	20172d1

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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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