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	123200dr	Isogeny class
Conductor	123200	Conductor
∏ cp	108	Product of Tamagawa factors cp
Δ	-4674897920000 = -1 · 214 · 54 · 73 · 113	Discriminant
Eigenvalues	2+ -1 5- 7- 11- -2 -3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,2767,86737]	[a1,a2,a3,a4,a6]
Generators	[53:616:1] [-13:220:1]	Generators of the group modulo torsion
j	228714800/456533	j-invariant
L	10.072912901684	L(r)(E,1)/r!
Ω	0.53340442936713	Real period
R	0.17485365119964	Regulator
r	2	Rank of the group of rational points
S	1.0000000001257	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	123200gs2 7700j2 123200q2	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 123200dr2

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
+	-1	-	-	-	-2	-3	-2	-6	-6	-7	-11	6	1	3	-9	3	10	-14	-6	11	11	0	6	8

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Quadratic twists for elliptic curve 123200dr2

-4	8	5
123200gs2	7700j2	123200q2

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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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