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	17424bg	Isogeny class
Conductor	17424	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	8064	Modular degree for the optimal curve
Δ	-1619177472 = -1 · 212 · 33 · 114	Discriminant
Eigenvalues	2- 3+  0 -5 11-  2  0  7	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,0,-1936]	[a1,a2,a3,a4,a6]
Generators	[25:117:1]	Generators of the group modulo torsion
j	0	j-invariant
L	4.0789112078796	L(r)(E,1)/r!
Ω	0.68793513194875	Real period
R	2.96460452334	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	1089a1 69696ek1 17424bg2 17424bf1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 17424bg1

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	-5	-	2	0	7	0	0	-11	11	0	-8	0	0	0	-1	-11	0	17	13	0	0	5

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Quadratic twists for elliptic curve 17424bg1

-4	8	-3	-11
1089a1	69696ek1	17424bg2	17424bf1

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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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