Cremona's table of elliptic curves

103488 = 2⁶ · 3 · 7² · 11

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 11-	Signs for the Atkin-Lehner involutions
Class	103488gk	Isogeny class
Conductor	103488	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	65536	Modular degree for the optimal curve
Δ	-13769699328 = -1 · 212 · 34 · 73 · 112	Discriminant
Eigenvalues	2- 3+ -2 7- 11-  0 -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,551,-2855]	[a1,a2,a3,a4,a6]
Generators	[7:36:1] [16:99:1]	Generators of the group modulo torsion
j	13144256/9801	j-invariant
L	8.8893705430264	L(r)(E,1)/r!
Ω	0.70258157281501	Real period
R	1.5815548838622	Regulator
r	2	Rank of the group of rational points
S	1.000000000073	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	103488hu1 51744bl1 103488ik1	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 103488gk1

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

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Quadratic twists for elliptic curve 103488gk1

-4	8	-7
103488hu1	51744bl1	103488ik1

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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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