Cremona's table of elliptic curves

5680 = 2⁴ · 5 · 71

Field	Data	Notes
Atkin-Lehner	2- 5- 71+	Signs for the Atkin-Lehner involutions
Class	5680i	Isogeny class
Conductor	5680	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	-90880 = -1 · 28 · 5 · 71	Discriminant
Eigenvalues	2- -2 5- -3  4 -1  2 -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-5,-17]	[a1,a2,a3,a4,a6]
Generators	[3:2:1]	Generators of the group modulo torsion
j	-65536/355	j-invariant
L	2.673373578757	L(r)(E,1)/r!
Ω	1.4124693671214	Real period
R	0.94634745396476	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	1420b1 22720bc1 51120bj1 28400n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5680i1

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	-	-3	4	-1	2	-1	-8	9	-10	0	6	6	1	-9	6	-10	4	+	4	11	-2	15	-17

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Quadratic twists for elliptic curve 5680i1

-4	8	-3	5
1420b1	22720bc1	51120bj1	28400n1

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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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