Cremona's table of elliptic curves

12775 = 5² · 7 · 73

Field	Data	Notes
Atkin-Lehner	5+ 7+ 73-	Signs for the Atkin-Lehner involutions
Class	12775b	Isogeny class
Conductor	12775	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	117600	Modular degree for the optimal curve
Δ	-201373956806640625 = -1 · 510 · 710 · 73	Discriminant
Eigenvalues	1  0 5+ 7+  3  4  2  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-100742,24877041]	[a1,a2,a3,a4,a6]
j	-11578646613825/20620693177	j-invariant
L	2.2690912750866	L(r)(E,1)/r!
Ω	0.28363640938582	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	114975v1 12775n1 89425h1	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 12775b1

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
1	0	+	+	3	4	2	8	4	2	-7	-11	-9	-7	1	10	-11	11	-12	10	-	6	11	-11	15

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Quadratic twists for elliptic curve 12775b1

-3	5	-7
114975v1	12775n1	89425h1

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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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