Cremona's table of elliptic curves

17424 = 2⁴ · 3² · 11²

Field	Data	Notes
Atkin-Lehner	2- 3- 11+	Signs for the Atkin-Lehner involutions
Class	17424bj	Isogeny class
Conductor	17424	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	304128	Modular degree for the optimal curve
Δ	1.2166492167066E+19	Discriminant
Eigenvalues	2- 3-  0  0 11+  6  6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-618915,83424418]	[a1,a2,a3,a4,a6]
Generators	[27377:4527936:1]	Generators of the group modulo torsion
j	3723875/1728	j-invariant
L	5.4084016874458	L(r)(E,1)/r!
Ω	0.20170401964488	Real period
R	6.7033885801677	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	2178b1 69696ey1 5808y1 17424bk1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 17424bj1

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
-	-	0	0	+	6	6	-6	6	-6	-4	-2	-6	-6	6	12	-12	6	-4	-6	-12	-12	0	6	-10

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Quadratic twists for elliptic curve 17424bj1

-4	8	-3	-11
2178b1	69696ey1	5808y1	17424bk1

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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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