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	123840bc	Isogeny class
Conductor	123840	Conductor
∏ cp	112	Product of Tamagawa factors cp
deg	4587520	Modular degree for the optimal curve
Δ	1857600000000000000 = 218 · 33 · 514 · 43	Discriminant
Eigenvalues	2+ 3+ 5-  4  4 -2 -6  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-5000172,-4303037264]	[a1,a2,a3,a4,a6]
Generators	[-1290:704:1]	Generators of the group modulo torsion
j	1953326569433829507/262451171875	j-invariant
L	10.213263248514	L(r)(E,1)/r!
Ω	0.10096173847889	Real period
R	3.6128478404206	Regulator
r	1	Rank of the group of rational points
S	1.0000000079617	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	123840ed1 1935a1 123840n1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 123840bc1

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
+	+	-	4	4	-2	-6	6	6	-2	-4	-8	-8	-	6	6	0	10	-12	-16	16	-4	6	-2	-18

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Quadratic twists for elliptic curve 123840bc1

-4	8	-3
123840ed1	1935a1	123840n1

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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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