Cremona's table of elliptic curves

5621 = 7 · 11 · 73

Field	Data	Notes
Atkin-Lehner	7- 11+ 73-	Signs for the Atkin-Lehner involutions
Class	5621c	Isogeny class
Conductor	5621	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1408	Modular degree for the optimal curve
Δ	-140744219 = -1 · 74 · 11 · 732	Discriminant
Eigenvalues	0 -1 -1 7- 11+  0  0  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-351,2715]	[a1,a2,a3,a4,a6]
Generators	[43:255:1]	Generators of the group modulo torsion
j	-4796028780544/140744219	j-invariant
L	2.3165406107483	L(r)(E,1)/r!
Ω	1.8322255930087	Real period
R	0.15804144284877	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	89936p1 50589o1 39347b1 61831b1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 5621c1

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	-1	-1	-	+	0	0	8	-5	-6	-7	7	-2	6	0	10	3	10	-3	13	-	-8	14	15	-11

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Quadratic twists for elliptic curve 5621c1

-4	-3	-7	-11
89936p1	50589o1	39347b1	61831b1

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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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