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	5680a	Isogeny class
Conductor	5680	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	448	Modular degree for the optimal curve
Δ	-454400 = -1 · 28 · 52 · 71	Discriminant
Eigenvalues	2+  0 5+  2 -4  4  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,17,-18]	[a1,a2,a3,a4,a6]
Generators	[17:72:1]	Generators of the group modulo torsion
j	2122416/1775	j-invariant
L	3.7053101951095	L(r)(E,1)/r!
Ω	1.6392315905457	Real period
R	2.2603945754095	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	2840e1 22720bh1 51120k1 28400a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5680a1

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	+	2	-4	4	0	4	-2	-6	0	2	6	4	-2	-12	12	6	-10	+	-14	0	0	2	-12

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Quadratic twists for elliptic curve 5680a1

-4	8	-3	5
2840e1	22720bh1	51120k1	28400a1

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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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