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	17424b	Isogeny class
Conductor	17424	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	36799488 = 210 · 33 · 113	Discriminant
Eigenvalues	2+ 3+  2 -2 11+  2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-99,242]	[a1,a2,a3,a4,a6]
Generators	[1:12:1]	Generators of the group modulo torsion
j	2916	j-invariant
L	5.3022464615136	L(r)(E,1)/r!
Ω	1.8907659069701	Real period
R	0.70107124868915	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	8712o1 69696dx1 17424d1 17424a1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 17424b1

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

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Quadratic twists for elliptic curve 17424b1

-4	8	-3	-11
8712o1	69696dx1	17424d1	17424a1

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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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