Cremona's table of elliptic curves

3050 = 2 · 5² · 61

Field	Data	Notes
Atkin-Lehner	2- 5- 61+	Signs for the Atkin-Lehner involutions
Class	3050l	Isogeny class
Conductor	3050	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	336	Modular degree for the optimal curve
Δ	-61000 = -1 · 23 · 53 · 61	Discriminant
Eigenvalues	2- -2 5- -2  2 -5  7  1	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,2,12]	[a1,a2,a3,a4,a6]
Generators	[2:4:1]	Generators of the group modulo torsion
j	6859/488	j-invariant
L	3.4122770149734	L(r)(E,1)/r!
Ω	2.6762923622366	Real period
R	0.21250026486404	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	24400x1 97600bi1 27450y1 3050b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3050l1

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	-	-2	2	-5	7	1	-2	3	5	-8	-3	1	-13	-8	-10	+	-1	-8	-10	15	12	-10	4

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Quadratic twists for elliptic curve 3050l1

-4	8	-3	5
24400x1	97600bi1	27450y1	3050b1

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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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