Cremona's table of elliptic curves

4136 = 2³ · 11 · 47

Field	Data	Notes
Atkin-Lehner	2+ 11- 47+	Signs for the Atkin-Lehner involutions
Class	4136b	Isogeny class
Conductor	4136	Conductor
∏ cp	40	Product of Tamagawa factors cp
deg	10560	Modular degree for the optimal curve
Δ	-91074984704 = -1 · 28 · 115 · 472	Discriminant
Eigenvalues	2+ -3 -1 -4 11- -4  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-6868,219556]	[a1,a2,a3,a4,a6]
Generators	[-27257610:196328066:357911] [-54:658:1]	Generators of the group modulo torsion
j	-139950548941824/355761659	j-invariant
L	2.7853472396265	L(r)(E,1)/r!
Ω	1.075254051518	Real period
R	0.064760212614237	Regulator
r	2	Rank of the group of rational points
S	1.0000000000006	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	8272b1 33088g1 37224l1 103400bl1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4136b1

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
+	-3	-1	-4	-	-4	0	-2	-9	6	-5	-1	-2	-8	+	-10	-13	-6	1	15	-16	-14	-8	-5	-15

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Quadratic twists for elliptic curve 4136b1

-4	8	-3	5	-11
8272b1	33088g1	37224l1	103400bl1	45496g1

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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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