Cremona's table of elliptic curves

65072 = 2⁴ · 7² · 83

Field	Data	Notes
Atkin-Lehner	2- 7+ 83+	Signs for the Atkin-Lehner involutions
Class	65072i	Isogeny class
Conductor	65072	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	23040	Modular degree for the optimal curve
Δ	-1632526336 = -1 · 213 · 74 · 83	Discriminant
Eigenvalues	2-  0 -3 7+  0  3 -2 -5	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-539,5194]	[a1,a2,a3,a4,a6]
Generators	[21:-56:1] [15:22:1]	Generators of the group modulo torsion
j	-1760913/166	j-invariant
L	8.4517309581584	L(r)(E,1)/r!
Ω	1.4643474198301	Real period
R	0.48097255039386	Regulator
r	2	Rank of the group of rational points
S	1.0000000000021	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	8134c1 65072w1	Quadratic twists by: -4 -7

Hecke Eigenvalues for elliptic curve 65072i1

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	-3	+	0	3	-2	-5	3	-2	-9	-2	2	1	-6	-14	-2	0	-4	10	-8	-8	+	-12	4

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Quadratic twists for elliptic curve 65072i1

-4	-7
8134c1	65072w1

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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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