Cremona's table of elliptic curves

76050 = 2 · 3² · 5² · 13²

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 13+	Signs for the Atkin-Lehner involutions
Class	76050cp	Isogeny class
Conductor	76050	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	1437696	Modular degree for the optimal curve
Δ	642241111257720000 = 26 · 39 · 54 · 138	Discriminant
Eigenvalues	2+ 3- 5-  2  3 13+  0  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-381042,82007316]	[a1,a2,a3,a4,a6]
Generators	[465:2049:1]	Generators of the group modulo torsion
j	16462225/1728	j-invariant
L	5.6001210373017	L(r)(E,1)/r!
Ω	0.27951286951087	Real period
R	0.83480369632702	Regulator
r	1	Rank of the group of rational points
S	0.99999999963824	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	25350dk1 76050ep1 76050fy1	Quadratic twists by: -3 5 13

Hecke Eigenvalues for elliptic curve 76050cp1

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	3	+	0	8	-9	-6	-4	11	0	-10	12	-6	-12	-1	8	9	-7	-4	-9	-12	17

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Quadratic twists for elliptic curve 76050cp1

-3	5	13
25350dk1	76050ep1	76050fy1

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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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