Cremona's table of elliptic curves

12450 = 2 · 3 · 5² · 83

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 83-	Signs for the Atkin-Lehner involutions
Class	12450n	Isogeny class
Conductor	12450	Conductor
∏ cp	128	Product of Tamagawa factors cp
deg	645120	Modular degree for the optimal curve
Δ	-1.2973918503375E+21	Discriminant
Eigenvalues	2- 3+ 5+  0  0  6 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,2641037,-522464719]	[a1,a2,a3,a4,a6]
Generators	[660615:4480594:3375]	Generators of the group modulo torsion
j	130384850244802923671/83033078421600000	j-invariant
L	6.2484613276099	L(r)(E,1)/r!
Ω	0.087657955352884	Real period
R	8.9102884365365	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	99600cp1 37350f1 2490e1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 12450n1

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	0	6	-6	4	0	-2	-8	-6	2	-8	-8	-10	0	-2	0	8	-6	0	-	14	2

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Quadratic twists for elliptic curve 12450n1

-4	-3	5
99600cp1	37350f1	2490e1

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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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