Cremona's table of elliptic curves

27192 = 2³ · 3 · 11 · 103

Field	Data	Notes
Atkin-Lehner	2+ 3- 11- 103+	Signs for the Atkin-Lehner involutions
Class	27192a	Isogeny class
Conductor	27192	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	13312	Modular degree for the optimal curve
Δ	163152 = 24 · 32 · 11 · 103	Discriminant
Eigenvalues	2+ 3- -2  4 11- -2  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-3399,-77418]	[a1,a2,a3,a4,a6]
Generators	[-803738334:-632568:23639903]	Generators of the group modulo torsion
j	271509473892352/10197	j-invariant
L	6.7336863899405	L(r)(E,1)/r!
Ω	0.62524628132629	Real period
R	10.769654440258	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	54384a1 81576k1	Quadratic twists by: -4 -3

Hecke Eigenvalues for elliptic curve 27192a1

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	4	-	-2	2	0	-8	6	0	-2	2	-4	-8	6	-12	6	-4	8	6	-12	-16	18	-14

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Quadratic twists for elliptic curve 27192a1

-4	-3
54384a1	81576k1

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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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