Cremona's table of elliptic curves

17340 = 2² · 3 · 5 · 17²

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 17+	Signs for the Atkin-Lehner involutions
Class	17340f	Isogeny class
Conductor	17340	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	7776	Modular degree for the optimal curve
Δ	-78030000 = -1 · 24 · 33 · 54 · 172	Discriminant
Eigenvalues	2- 3+ 5-  1  0  5 17+ -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1745,28650]	[a1,a2,a3,a4,a6]
Generators	[25:-5:1]	Generators of the group modulo torsion
j	-127157223424/16875	j-invariant
L	4.9414437028362	L(r)(E,1)/r!
Ω	1.8615306670186	Real period
R	0.22120880549116	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	69360dq1 52020q1 86700bh1 17340o1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 17340f1

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
-	+	-	1	0	5	+	-1	-6	0	-5	1	0	5	-12	12	12	1	-13	-6	-2	-8	-6	-6	-17

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Quadratic twists for elliptic curve 17340f1

-4	-3	5	17
69360dq1	52020q1	86700bh1	17340o1

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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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