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	17472j	Isogeny class
Conductor	17472	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	61440	Modular degree for the optimal curve
Δ	-242424916651008 = -1 · 210 · 35 · 78 · 132	Discriminant
Eigenvalues	2+ 3+  0 7-  2 13- -6  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-41293,3329245]	[a1,a2,a3,a4,a6]
Generators	[108:343:1]	Generators of the group modulo torsion
j	-7604375980288000/236743082667	j-invariant
L	4.5529732786297	L(r)(E,1)/r!
Ω	0.55333266588218	Real period
R	1.0285343608286	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	17472cr1 2184f1 52416cs1 122304cs1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 17472j1

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

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Quadratic twists for elliptic curve 17472j1

-4	8	-3	-7
17472cr1	2184f1	52416cs1	122304cs1

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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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