Cremona's table of elliptic curves

136 = 2³ · 17

Field	Data	Notes
Atkin-Lehner	2- 17-	Signs for the Atkin-Lehner involutions
Class	136a	Isogeny class
Conductor	136	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	8	Modular degree for the optimal curve
Δ	4352 = 28 · 17	Discriminant
Eigenvalues	2- -2 -2 -2 -6  2 17-  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-4,0]	[a1,a2,a3,a4,a6]
Generators	[-2:2:1]	Generators of the group modulo torsion
j	35152/17	j-invariant
L	0.89989598753536	L(r)(E,1)/r!
Ω	3.8871054798095	Real period
R	0.23150799282644	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	272c1 1088f1 1224b1 3400c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 136a1

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	-6	2	-	0	6	-10	2	6	-6	-8	0	-10	-8	14	4	2	-14	-10	8	-10	2

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Quadratic twists for elliptic curve 136a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29
272c1	1088f1	1224b1	3400c1	6664d1	16456e1	22984e1	2312c1	49096d1	71944d1	114376b1

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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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