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	13872be	Isogeny class
Conductor	13872	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	165888	Modular degree for the optimal curve
Δ	78416941578190848 = 218 · 36 · 177	Discriminant
Eigenvalues	2- 3-  0  2  0  2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1181528,-494537196]	[a1,a2,a3,a4,a6]
Generators	[-620:258:1]	Generators of the group modulo torsion
j	1845026709625/793152	j-invariant
L	6.3446137473764	L(r)(E,1)/r!
Ω	0.14481039041682	Real period
R	3.6511041145563	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	1734b1 55488cd1 41616bx1 816e1	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for elliptic curve 13872be1

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	0	2	+	4	-6	0	-10	-8	-6	4	-12	6	12	-8	4	6	-2	-10	-12	-18	-14

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Quadratic twists for elliptic curve 13872be1

-4	8	-3	17
1734b1	55488cd1	41616bx1	816e1

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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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