Cremona's table of elliptic curves

13454 = 2 · 7 · 31²

Field	Data	Notes
Atkin-Lehner	2+ 7- 31-	Signs for the Atkin-Lehner involutions
Class	13454c	Isogeny class
Conductor	13454	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	9984	Modular degree for the optimal curve
Δ	-83708420096 = -1 · 213 · 73 · 313	Discriminant
Eigenvalues	2+ -1  1 7- -4  2  2 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,523,13357]	[a1,a2,a3,a4,a6]
Generators	[-3:110:1]	Generators of the group modulo torsion
j	529475129/2809856	j-invariant
L	2.8391985840637	L(r)(E,1)/r!
Ω	0.77811975957202	Real period
R	0.60813230635717	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	107632f1 121086bg1 94178e1 13454b1	Quadratic twists by: -4 -3 -7 -31

Hecke Eigenvalues for elliptic curve 13454c1

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	1	-	-4	2	2	-2	-3	9	-	-2	-2	-8	7	2	6	2	5	-6	-1	7	13	-17	-10

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Quadratic twists for elliptic curve 13454c1

-4	-3	-7	-31
107632f1	121086bg1	94178e1	13454b1

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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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