Cremona's table of elliptic curves

2072 = 2³ · 7 · 37

Field	Data	Notes
Atkin-Lehner	2+ 7+ 37+	Signs for the Atkin-Lehner involutions
Class	2072c	Isogeny class
Conductor	2072	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	864	Modular degree for the optimal curve
Δ	-480836608 = -1 · 210 · 73 · 372	Discriminant
Eigenvalues	2+  2 -2 7+  4 -6 -4  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,16,-1060]	[a1,a2,a3,a4,a6]
Generators	[298:5136:1]	Generators of the group modulo torsion
j	415292/469567	j-invariant
L	3.6152479315744	L(r)(E,1)/r!
Ω	0.77298255157735	Real period
R	4.6770110453297	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	4144e1 16576f1 18648z1 51800s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2072c1

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	-2	+	4	-6	-4	4	0	-10	2	+	-2	-4	0	6	0	-14	12	-8	-14	12	6	0	-8

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Quadratic twists for elliptic curve 2072c1

-4	8	-3	5	-7	37
4144e1	16576f1	18648z1	51800s1	14504f1	76664i1

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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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