Cremona's table of elliptic curves

124992 = 2⁶ · 3² · 7 · 31

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 31+	Signs for the Atkin-Lehner involutions
Class	124992er	Isogeny class
Conductor	124992	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	110592	Modular degree for the optimal curve
Δ	-199277620416 = -1 · 26 · 315 · 7 · 31	Discriminant
Eigenvalues	2- 3- -3 7+  0 -5  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,816,-19514]	[a1,a2,a3,a4,a6]
Generators	[27:149:1]	Generators of the group modulo torsion
j	1287913472/4271211	j-invariant
L	4.0027812222837	L(r)(E,1)/r!
Ω	0.51263385765308	Real period
R	3.9041327539702	Regulator
r	1	Rank of the group of rational points
S	0.99999998835028	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	124992dk1 31248bk1 41664dh1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 124992er1

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
-	-	-3	+	0	-5	0	2	3	3	+	-2	-9	8	0	-3	12	1	5	-6	-7	-8	-6	12	-10

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Quadratic twists for elliptic curve 124992er1

-4	8	-3
124992dk1	31248bk1	41664dh1

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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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