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	8120b	Isogeny class
Conductor	8120	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	82418000 = 24 · 53 · 72 · 292	Discriminant
Eigenvalues	2+ -2 5+ 7+  0 -2  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-2051,35074]	[a1,a2,a3,a4,a6]
Generators	[-3:203:1]	Generators of the group modulo torsion
j	59664010307584/5151125	j-invariant
L	2.3791102361066	L(r)(E,1)/r!
Ω	1.8363940679716	Real period
R	0.64776680495774	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	16240c1 64960n1 73080bm1 40600s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8120b1

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	-2	0	4	-4	+	-4	4	2	-10	10	10	-12	-10	12	0	12	0	12	2	8

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Quadratic twists for elliptic curve 8120b1

-4	8	-3	5	-7
16240c1	64960n1	73080bm1	40600s1	56840d1

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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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