Cremona's table of elliptic curves

5520 = 2⁴ · 3 · 5 · 23

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 23-	Signs for the Atkin-Lehner involutions
Class	5520w	Isogeny class
Conductor	5520	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	7680	Modular degree for the optimal curve
Δ	-77262336000 = -1 · 212 · 38 · 53 · 23	Discriminant
Eigenvalues	2- 3+ 5-  5  2 -6  1 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1605,-27603]	[a1,a2,a3,a4,a6]
j	-111701610496/18862875	j-invariant
L	2.2420015373211	L(r)(E,1)/r!
Ω	0.37366692288685	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	345f1 22080cu1 16560bo1 27600cs1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5520w1

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
-	+	-	5	2	-6	1	-2	-	-1	5	-7	-7	8	12	9	-3	12	1	-5	-2	8	-3	8	14

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Quadratic twists for elliptic curve 5520w1

-4	8	-3	5	-23
345f1	22080cu1	16560bo1	27600cs1	126960bo1

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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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