Elliptic curve isogeny class with LMFDB label 86151.e (Cremona label 86151a)

• Label: 86151.e
• Number of curves: $4$
• Conductor: $86151$
• CM: no
• Rank: $0$

Elliptic curves in class 86151.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
86151.e1	86151a4	\([1, 1, 0, -153571, 23099476]\)	\(37159393753/1053\)	\(11350513741437\)	\([2]\)	\(423936\)	\(1.6067\)
86151.e2	86151a3	\([1, 1, 0, -43121, -3139026]\)	\(822656953/85683\)	\(923595507034707\)	\([2]\)	\(423936\)	\(1.6067\)
86151.e3	86151a2	\([1, 1, 0, -9986, 326895]\)	\(10218313/1521\)	\(16395186515409\)	\([2, 2]\)	\(211968\)	\(1.2601\)
86151.e4	86151a1	\([1, 1, 0, 1059, 28680]\)	\(12167/39\)	\(-420389397831\)	\([2]\)	\(105984\)	\(0.91356\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 86151.e have rank \(0\).

Complex multiplication

The elliptic curves in class 86151.e do not have complex multiplication.

Modular form 86151.2.a.e

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.