Cremona's table of elliptic curves

117117 = 3² · 7 · 11 · 13²

Field	Data	Notes
Atkin-Lehner	3+ 7+ 11+ 13-	Signs for the Atkin-Lehner involutions
Class	117117c	Isogeny class
Conductor	117117	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	33408	Modular degree for the optimal curve
Δ	-4567563 = -1 · 33 · 7 · 11 · 133	Discriminant
Eigenvalues	-2 3+ -2 7+ 11+ 13-  2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,39,42]	[a1,a2,a3,a4,a6]
Generators	[-1:1:1] [0:6:1]	Generators of the group modulo torsion
j	110592/77	j-invariant
L	5.0213210101388	L(r)(E,1)/r!
Ω	1.5473566207519	Real period
R	0.81127403658551	Regulator
r	2	Rank of the group of rational points
S	1.0000000006213	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	117117f1 117117j1	Quadratic twists by: -3 13

Hecke Eigenvalues for elliptic curve 117117c1

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	+	-2	+	+	-	2	-6	-2	-9	9	-4	3	2	-12	0	10	-13	8	-13	-14	-4	-11	12	9

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Quadratic twists for elliptic curve 117117c1

-3	13
117117f1	117117j1

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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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