Cremona's table of elliptic curves

120640 = 2⁶ · 5 · 13 · 29

Field	Data	Notes
Atkin-Lehner	2+ 5- 13+ 29-	Signs for the Atkin-Lehner involutions
Class	120640bg	Isogeny class
Conductor	120640	Conductor
∏ cp	120	Product of Tamagawa factors cp
deg	1720320	Modular degree for the optimal curve
Δ	321680451996800000 = 210 · 55 · 132 · 296	Discriminant
Eigenvalues	2+ -2 5-  0 -4 13+  4  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-736685,241592083]	[a1,a2,a3,a4,a6]
Generators	[-314:21025:1]	Generators of the group modulo torsion
j	43178726198367422464/314141066403125	j-invariant
L	4.6154112677915	L(r)(E,1)/r!
Ω	0.30684003516743	Real period
R	0.50139168331566	Regulator
r	1	Rank of the group of rational points
S	1.0000000033701	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	120640cq1 15080a1	Quadratic twists by: -4 8

Hecke Eigenvalues for elliptic curve 120640bg1

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

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Quadratic twists for elliptic curve 120640bg1

-4	8
120640cq1	15080a1

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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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