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	13872bd	Isogeny class
Conductor	13872	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-930934161408 = -1 · 230 · 3 · 172	Discriminant
Eigenvalues	2- 3-  0 -1  0 -1 17+  7	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-3768,99156]	[a1,a2,a3,a4,a6]
Generators	[1218:4096:27]	Generators of the group modulo torsion
j	-4999353625/786432	j-invariant
L	5.6349058607822	L(r)(E,1)/r!
Ω	0.85226634241746	Real period
R	1.6529181021037	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	1734a2 55488bz2 41616bw2 13872z2	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for elliptic curve 13872bd2

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	-1	0	-1	+	7	-6	0	5	-5	12	-11	6	-12	-6	-5	7	-12	-2	8	6	0	7

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Quadratic twists for elliptic curve 13872bd2

-4	8	-3	17
1734a2	55488bz2	41616bw2	13872z2

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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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