Cremona's table of elliptic curves

127890 = 2 · 3² · 5 · 7² · 29

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 7+ 29+	Signs for the Atkin-Lehner involutions
Class	127890dr	Isogeny class
Conductor	127890	Conductor
∏ cp	108	Product of Tamagawa factors cp
deg	158976	Modular degree for the optimal curve
Δ	15039864000 = 26 · 33 · 53 · 74 · 29	Discriminant
Eigenvalues	2- 3+ 5- 7+  0 -4  6 -7	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-2582,50789]	[a1,a2,a3,a4,a6]
Generators	[-33:331:1]	Generators of the group modulo torsion
j	29354778243/232000	j-invariant
L	11.441147455233	L(r)(E,1)/r!
Ω	1.2522891268911	Real period
R	0.76134889384005	Regulator
r	1	Rank of the group of rational points
S	1.000000013715	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	127890a2 127890di1	Quadratic twists by: -3 -7

Hecke Eigenvalues for elliptic curve 127890dr1

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
-	+	-	+	0	-4	6	-7	-6	+	5	-7	9	8	-3	-9	3	-10	-7	15	-1	8	6	3	-7

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Quadratic twists for elliptic curve 127890dr1

-3	-7
127890a2	127890di1

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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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