Cremona's table of elliptic curves

14703 = 3 · 13² · 29

Field	Data	Notes
Atkin-Lehner	3- 13+ 29-	Signs for the Atkin-Lehner involutions
Class	14703f	Isogeny class
Conductor	14703	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	23040	Modular degree for the optimal curve
Δ	-60601957923 = -1 · 3 · 134 · 294	Discriminant
Eigenvalues	0 3- -2 -5  2 13+ -4  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-6309,191156]	[a1,a2,a3,a4,a6]
Generators	[-22:565:1]	Generators of the group modulo torsion
j	-972524879872/2121843	j-invariant
L	2.9721305440035	L(r)(E,1)/r!
Ω	1.11133315973	Real period
R	0.22286525257088	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	44109n1 14703e1	Quadratic twists by: -3 13

Hecke Eigenvalues for elliptic curve 14703f1

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	-5	2	+	-4	4	-6	-	9	2	-12	-5	-6	0	6	3	15	6	5	-1	-8	12	9

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Quadratic twists for elliptic curve 14703f1

-3	13
44109n1	14703e1

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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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