Cremona's table of elliptic curves

13728 = 2⁵ · 3 · 11 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3+ 11- 13-	Signs for the Atkin-Lehner involutions
Class	13728d	Isogeny class
Conductor	13728	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	8566272 = 29 · 32 · 11 · 132	Discriminant
Eigenvalues	2+ 3+ -2  0 11- 13-  0  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-104,420]	[a1,a2,a3,a4,a6]
Generators	[-8:26:1]	Generators of the group modulo torsion
j	245314376/16731	j-invariant
L	3.4938533065833	L(r)(E,1)/r!
Ω	2.2778151925984	Real period
R	0.76693081114227	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	13728i2 27456w2 41184ba2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 13728d2

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

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Quadratic twists for elliptic curve 13728d2

-4	8	-3
13728i2	27456w2	41184ba2

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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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