Cremona's table of elliptic curves

8120 = 2³ · 5 · 7 · 29

Field	Data	Notes
Atkin-Lehner	2+ 5+ 7- 29-	Signs for the Atkin-Lehner involutions
Class	8120c	Isogeny class
Conductor	8120	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	640	Modular degree for the optimal curve
Δ	-470960 = -1 · 24 · 5 · 7 · 292	Discriminant
Eigenvalues	2+  0 5+ 7-  0 -2 -6  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,2,33]	[a1,a2,a3,a4,a6]
Generators	[1:6:1]	Generators of the group modulo torsion
j	55296/29435	j-invariant
L	3.8080943952637	L(r)(E,1)/r!
Ω	2.301793644309	Real period
R	1.6544030368139	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	16240b1 64960r1 73080br1 40600o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8120c1

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

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Quadratic twists for elliptic curve 8120c1

-4	8	-3	5	-7
16240b1	64960r1	73080br1	40600o1	56840h1

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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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