Cremona's table of elliptic curves

13872 = 2⁴ · 3 · 17²

Field	Data	Notes
Atkin-Lehner	2+ 3+ 17-	Signs for the Atkin-Lehner involutions
Class	13872f	Isogeny class
Conductor	13872	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	12960	Modular degree for the optimal curve
Δ	-4618377216 = -1 · 211 · 33 · 174	Discriminant
Eigenvalues	2+ 3+  1 -4 -3  2 17-  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-4720,-123296]	[a1,a2,a3,a4,a6]
j	-68001122/27	j-invariant
L	0.57596493475693	L(r)(E,1)/r!
Ω	0.28798246737846	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6936o1 55488ee1 41616bg1 13872l1	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for elliptic curve 13872f1

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	-4	-3	2	-	0	-6	-1	-5	0	6	-4	6	-13	-7	-10	14	-8	1	-11	4	8	-13

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Quadratic twists for elliptic curve 13872f1

-4	8	-3	17
6936o1	55488ee1	41616bg1	13872l1

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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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