Cremona's table of elliptic curves

123840 = 2⁶ · 3² · 5 · 43

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5- 43-	Signs for the Atkin-Lehner involutions
Class	123840w	Isogeny class
Conductor	123840	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	1022423040000 = 215 · 33 · 54 · 432	Discriminant
Eigenvalues	2+ 3+ 5-  2  2 -2  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-80172,-8737264]	[a1,a2,a3,a4,a6]
Generators	[-163:5:1]	Generators of the group modulo torsion
j	64413688156056/1155625	j-invariant
L	8.6930665291799	L(r)(E,1)/r!
Ω	0.283722868967	Real period
R	1.914955460744	Regulator
r	1	Rank of the group of rational points
S	1.0000000014861	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	123840t2 61920b2 123840i2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 123840w2

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
+	+	-	2	2	-2	0	0	4	-6	4	-8	-8	-	-4	-2	2	8	12	8	-2	-8	-6	6	-18

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Quadratic twists for elliptic curve 123840w2

-4	8	-3
123840t2	61920b2	123840i2

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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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