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	76050cc	Isogeny class
Conductor	76050	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	57600	Modular degree for the optimal curve
Δ	-19459597950 = -1 · 2 · 311 · 52 · 133	Discriminant
Eigenvalues	2+ 3- 5+  2  0 13- -2 -1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-2547,50571]	[a1,a2,a3,a4,a6]
Generators	[75:489:1]	Generators of the group modulo torsion
j	-45646645/486	j-invariant
L	5.0047102030241	L(r)(E,1)/r!
Ω	1.2247331996674	Real period
R	0.5107959640953	Regulator
r	1	Rank of the group of rational points
S	0.99999999983119	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	25350dd1 76050gi2 76050fj1	Quadratic twists by: -3 5 13

Hecke Eigenvalues for elliptic curve 76050cc1

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	0	-	-2	-1	4	-5	0	7	-5	-4	-7	-9	4	12	-7	-5	4	5	4	14	-2

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Quadratic twists for elliptic curve 76050cc1

-3	5	13
25350dd1	76050gi2	76050fj1

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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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