Cremona's table of elliptic curves

13050 = 2 · 3² · 5² · 29

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 29+	Signs for the Atkin-Lehner involutions
Class	13050r	Isogeny class
Conductor	13050	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	11035602000 = 24 · 38 · 53 · 292	Discriminant
Eigenvalues	2+ 3- 5- -2  4 -4 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-34587,-2467179]	[a1,a2,a3,a4,a6]
Generators	[-107:54:1]	Generators of the group modulo torsion
j	50214820613957/121104	j-invariant
L	3.0811444073963	L(r)(E,1)/r!
Ω	0.35008282546669	Real period
R	2.200296746412	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	104400fn2 4350bb2 13050br2	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 13050r2

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	4	-4	-6	-4	6	+	8	-2	6	0	-4	4	12	-14	2	16	-6	4	14	6	-2

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Quadratic twists for elliptic curve 13050r2

-4	-3	5
104400fn2	4350bb2	13050br2

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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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