Cremona's table of elliptic curves

17472 = 2⁶ · 3 · 7 · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 13+	Signs for the Atkin-Lehner involutions
Class	17472ce	Isogeny class
Conductor	17472	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	15360	Modular degree for the optimal curve
Δ	8858304 = 26 · 32 · 7 · 133	Discriminant
Eigenvalues	2- 3+ -2 7-  0 13+ -4  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-20504,1136934]	[a1,a2,a3,a4,a6]
Generators	[-25:1278:1]	Generators of the group modulo torsion
j	14896378491692608/138411	j-invariant
L	3.4540777249885	L(r)(E,1)/r!
Ω	1.6129640042377	Real period
R	4.2828949882499	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	17472cn1 8736z2 52416fx1 122304id1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 17472ce1

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	-	0	+	-4	4	-6	6	0	6	-6	-4	-2	6	6	14	4	-4	6	4	6	-2	-6

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Quadratic twists for elliptic curve 17472ce1

-4	8	-3	-7
17472cn1	8736z2	52416fx1	122304id1

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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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