Cremona's table of elliptic curves

10224 = 2⁴ · 3² · 71

Field	Data	Notes
Atkin-Lehner	2+ 3- 71+	Signs for the Atkin-Lehner involutions
Class	10224a	Isogeny class
Conductor	10224	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	-86935244544 = -1 · 28 · 314 · 71	Discriminant
Eigenvalues	2+ 3-  2  0  0 -6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-759,16310]	[a1,a2,a3,a4,a6]
j	-259108432/465831	j-invariant
L	1.9233709486304	L(r)(E,1)/r!
Ω	0.96168547431519	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	5112a1 40896bp1 3408a1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 10224a1

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	0	0	-6	-2	-4	0	2	8	-2	6	4	-8	-2	8	2	8	+	-6	16	12	6	10

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Quadratic twists for elliptic curve 10224a1

-4	8	-3
5112a1	40896bp1	3408a1

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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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