Cremona's table of elliptic curves

5124 = 2² · 3 · 7 · 61

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 61-	Signs for the Atkin-Lehner involutions
Class	5124a	Isogeny class
Conductor	5124	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1440	Modular degree for the optimal curve
Δ	-78766128 = -1 · 24 · 33 · 72 · 612	Discriminant
Eigenvalues	2- 3+  0 7+  4 -6  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-133,-686]	[a1,a2,a3,a4,a6]
Generators	[266:4326:1]	Generators of the group modulo torsion
j	-16384000000/4922883	j-invariant
L	3.2064526764239	L(r)(E,1)/r!
Ω	0.69179026265755	Real period
R	4.6350069515378	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	20496z1 81984s1 15372c1 128100u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5124a1

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	+	4	-6	6	-4	4	4	-4	-2	-8	-4	-4	12	6	-	4	8	-2	-8	-4	-2	-2

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Quadratic twists for elliptic curve 5124a1

-4	8	-3	5	-7
20496z1	81984s1	15372c1	128100u1	35868g1

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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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