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	103488ef	Isogeny class
Conductor	103488	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	4723006869504 = 212 · 34 · 76 · 112	Discriminant
Eigenvalues	2+ 3- -2 7- 11- -6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-6729,-187209]	[a1,a2,a3,a4,a6]
Generators	[-57:120:1] [-54:147:1]	Generators of the group modulo torsion
j	69934528/9801	j-invariant
L	12.092449183285	L(r)(E,1)/r!
Ω	0.53202723627434	Real period
R	2.8411255004107	Regulator
r	2	Rank of the group of rational points
S	1.0000000000123	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	103488bf2 51744by1 2112f2	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 103488ef2

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	-4	-4	-2	4	2	-10	4	4	-6	-12	-6	4	-4	-10	-16	4	-10	-2

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Quadratic twists for elliptic curve 103488ef2

-4	8	-7
103488bf2	51744by1	2112f2

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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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