Cremona's table of elliptic curves

2272 = 2⁵ · 71

Field	Data	Notes
Atkin-Lehner	2+ 71+	Signs for the Atkin-Lehner involutions
Class	2272a	Isogeny class
Conductor	2272	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	160	Modular degree for the optimal curve
Δ	36352 = 29 · 71	Discriminant
Eigenvalues	2+ -1  0  3 -4  5 -8  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-8,4]	[a1,a2,a3,a4,a6]
Generators	[0:2:1]	Generators of the group modulo torsion
j	125000/71	j-invariant
L	2.7708084193711	L(r)(E,1)/r!
Ω	3.1462513868258	Real period
R	0.44033487453882	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	2272c1 4544a1 20448k1 56800k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2272a1

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	0	3	-4	5	-8	1	7	4	-7	-4	-12	1	-3	2	-6	-2	8	+	7	0	12	-11	-8

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Quadratic twists for elliptic curve 2272a1

-4	8	-3	5	-7
2272c1	4544a1	20448k1	56800k1	111328g1

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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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