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	17472cc	Isogeny class
Conductor	17472	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	46080	Modular degree for the optimal curve
Δ	-169011337936896 = -1 · 214 · 34 · 73 · 135	Discriminant
Eigenvalues	2- 3+  1 7-  2 13+ -4  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-7925,-679251]	[a1,a2,a3,a4,a6]
Generators	[260:3843:1]	Generators of the group modulo torsion
j	-3360132358144/10315633419	j-invariant
L	4.7424746128674	L(r)(E,1)/r!
Ω	0.23362951693684	Real period
R	3.3831873893382	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	17472v1 4368ba1 52416fw1 122304ia1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 17472cc1

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	-	2	+	-4	1	3	-3	-5	8	-10	1	13	1	-8	14	2	-4	-7	-17	-9	5	13

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Quadratic twists for elliptic curve 17472cc1

-4	8	-3	-7
17472v1	4368ba1	52416fw1	122304ia1

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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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