Cremona's table of elliptic curves

17136 = 2⁴ · 3² · 7 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 17-	Signs for the Atkin-Lehner involutions
Class	17136bs	Isogeny class
Conductor	17136	Conductor
∏ cp	40	Product of Tamagawa factors cp
deg	161280	Modular degree for the optimal curve
Δ	-102566103517495296 = -1 · 219 · 39 · 7 · 175	Discriminant
Eigenvalues	2- 3- -3 7-  1  1 17- -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-317379,-70523966]	[a1,a2,a3,a4,a6]
Generators	[737:9792:1]	Generators of the group modulo torsion
j	-1184052061112257/34349180544	j-invariant
L	4.0373138096667	L(r)(E,1)/r!
Ω	0.10039974116087	Real period
R	1.0053098152907	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	2142f1 68544ey1 5712x1 119952fk1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 17136bs1

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	1	-	-6	-2	2	0	5	-4	9	0	-11	4	6	11	-12	-5	15	1	-9	-9

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Quadratic twists for elliptic curve 17136bs1

-4	8	-3	-7
2142f1	68544ey1	5712x1	119952fk1

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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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