Cremona's table of elliptic curves

123200 = 2⁶ · 5² · 7 · 11

Field	Data	Notes
Atkin-Lehner	2+ 5+ 7+ 11-	Signs for the Atkin-Lehner involutions
Class	123200m	Isogeny class
Conductor	123200	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	73728	Modular degree for the optimal curve
Δ	-54208000000 = -1 · 212 · 56 · 7 · 112	Discriminant
Eigenvalues	2+  0 5+ 7+ 11- -2 -4 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-500,12000]	[a1,a2,a3,a4,a6]
Generators	[-19:121:1] [6:96:1]	Generators of the group modulo torsion
j	-216000/847	j-invariant
L	11.222990743827	L(r)(E,1)/r!
Ω	0.9773815087739	Real period
R	2.8706780937499	Regulator
r	2	Rank of the group of rational points
S	0.99999999981582	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	123200bi1 61600b1 4928l1	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 123200m1

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	+	+	-	-2	-4	-2	0	-2	-10	10	-4	-8	6	-2	-4	10	-12	-4	-4	0	-14	-14	-2

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Quadratic twists for elliptic curve 123200m1

-4	8	5
123200bi1	61600b1	4928l1

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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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