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	8120a	Isogeny class
Conductor	8120	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	15360	Modular degree for the optimal curve
Δ	7469131250000 = 24 · 58 · 72 · 293	Discriminant
Eigenvalues	2+  2 5+ 7+  4 -2  0 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-6671,165620]	[a1,a2,a3,a4,a6]
Generators	[19:213:1]	Generators of the group modulo torsion
j	2052303811262464/466820703125	j-invariant
L	5.5110658914858	L(r)(E,1)/r!
Ω	0.69960438963948	Real period
R	3.9387016241606	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	16240e1 64960q1 73080bq1 40600t1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8120a1

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

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Quadratic twists for elliptic curve 8120a1

-4	8	-3	5	-7
16240e1	64960q1	73080bq1	40600t1	56840g1

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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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