Cremona's table of elliptic curves

12120 = 2³ · 3 · 5 · 101

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5- 101-	Signs for the Atkin-Lehner involutions
Class	12120f	Isogeny class
Conductor	12120	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	736	Modular degree for the optimal curve
Δ	-24240 = -1 · 24 · 3 · 5 · 101	Discriminant
Eigenvalues	2+ 3+ 5-  1  1  0 -7 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,5,-8]	[a1,a2,a3,a4,a6]
Generators	[3:5:1]	Generators of the group modulo torsion
j	702464/1515	j-invariant
L	4.291113451125	L(r)(E,1)/r!
Ω	1.967199585042	Real period
R	1.090665503326	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	24240o1 96960y1 36360n1 60600bf1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12120f1

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
+	+	-	1	1	0	-7	-5	1	6	5	2	9	-8	1	-14	0	0	-3	0	11	11	-4	-5	10

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Quadratic twists for elliptic curve 12120f1

-4	8	-3	5
24240o1	96960y1	36360n1	60600bf1

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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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