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	17424p	Isogeny class
Conductor	17424	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	7680	Modular degree for the optimal curve
Δ	-5487305472 = -1 · 28 · 311 · 112	Discriminant
Eigenvalues	2+ 3-  0 -1 11- -6  4 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-660,7436]	[a1,a2,a3,a4,a6]
Generators	[25:81:1]	Generators of the group modulo torsion
j	-1408000/243	j-invariant
L	4.5087516251499	L(r)(E,1)/r!
Ω	1.3040592759315	Real period
R	0.86436861198836	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	8712v1 69696fl1 5808d1 17424o1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 17424p1

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	-1	-	-6	4	-1	-2	6	3	7	2	4	-6	2	10	1	3	-4	3	5	-14	-16	13

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Quadratic twists for elliptic curve 17424p1

-4	8	-3	-11
8712v1	69696fl1	5808d1	17424o1

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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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