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
Δ	-2453248 = -1 · 28 · 7 · 372	Discriminant
Eigenvalues	2+  0  0 7+  4  0 -4  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,25,58]	[a1,a2,a3,a4,a6]
Generators	[7:24:1]	Generators of the group modulo torsion
j	6750000/9583	j-invariant
L	2.9633404622811	L(r)(E,1)/r!
Ω	1.7438610366407	Real period
R	1.6992985106139	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	4144a2 16576a2 18648u2 51800q2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2072a2

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 2072a2

-4	8	-3	5	-7	37
4144a2	16576a2	18648u2	51800q2	14504a2	76664f2

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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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