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	3050k	Isogeny class
Conductor	3050	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	1905152000 = 212 · 53 · 612	Discriminant
Eigenvalues	2-  2 5- -4 -4 -4  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-109233,-13941169]	[a1,a2,a3,a4,a6]
Generators	[495:7072:1]	Generators of the group modulo torsion
j	1153122726940210853/15241216	j-invariant
L	5.7438118880964	L(r)(E,1)/r!
Ω	0.26260988467514	Real period
R	1.8226693609299	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	24400bb2 97600bo2 27450bb2 3050c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3050k2

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	-4	2	4	-4	-6	-4	-10	6	8	-2	2	8	+	-8	-8	4	0	-6	-10	-16

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Quadratic twists for elliptic curve 3050k2

-4	8	-3	5
24400bb2	97600bo2	27450bb2	3050c2

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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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