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	2072a	Isogeny class
Conductor	2072	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	112	Modular degree for the optimal curve
Δ	29008 = 24 · 72 · 37	Discriminant
Eigenvalues	2+  0  0 7+  4  0 -4  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-10,9]	[a1,a2,a3,a4,a6]
Generators	[0:3:1]	Generators of the group modulo torsion
j	6912000/1813	j-invariant
L	2.9633404622811	L(r)(E,1)/r!
Ω	3.4877220732814	Real period
R	0.84964925530693	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	4144a1 16576a1 18648u1 51800q1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2072a1

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	+	4	0	-4	2	-4	10	-6	+	-6	4	-12	-6	-2	12	-12	-8	2	-12	-16	12	-8

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Quadratic twists for elliptic curve 2072a1

-4	8	-3	5	-7	37
4144a1	16576a1	18648u1	51800q1	14504a1	76664f1

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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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