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	17424bd	Isogeny class
Conductor	17424	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	1388340284153315328 = 214 · 33 · 1112	Discriminant
Eigenvalues	2- 3+  0  2 11- -2 -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-284955,-14633014]	[a1,a2,a3,a4,a6]
Generators	[-505:694:1]	Generators of the group modulo torsion
j	13060888875/7086244	j-invariant
L	5.1562167532118	L(r)(E,1)/r!
Ω	0.22033628870411	Real period
R	5.8503943943343	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	2178g2 69696ef2 17424bc4 1584h2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 17424bd2

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	2	-	-2	-6	2	0	-6	4	2	6	-10	12	12	12	10	-8	12	-14	2	12	0	2

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Quadratic twists for elliptic curve 17424bd2

-4	8	-3	-11
2178g2	69696ef2	17424bc4	1584h2

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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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