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	103488ir	Isogeny class
Conductor	103488	Conductor
∏ cp	72	Product of Tamagawa factors cp
deg	8847360	Modular degree for the optimal curve
Δ	3394267603550208 = 214 · 33 · 78 · 113	Discriminant
Eigenvalues	2- 3-  2 7- 11- -6  2  8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-115046577,-475000133553]	[a1,a2,a3,a4,a6]
Generators	[152082213:-19248345600:6859]	Generators of the group modulo torsion
j	87364831012240243408/1760913	j-invariant
L	10.309390171442	L(r)(E,1)/r!
Ω	0.046097898674744	Real period
R	12.42451203161	Regulator
r	1	Rank of the group of rational points
S	1.0000000029632	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	103488x1 25872f1 14784bv1	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 103488ir1

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	-	-	-6	2	8	4	-2	-8	-6	2	8	-4	-2	12	10	-12	12	-10	8	-12	-10	14

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Quadratic twists for elliptic curve 103488ir1

-4	8	-7
103488x1	25872f1	14784bv1

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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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