Elliptic curve isogeny class with Cremona label 84150eu (LMFDB label 84150.er)

• Label: 84150eu
• Number of curves: $4$
• Conductor: $84150$
• CM: no
• Rank: $1$

Elliptic curves in class 84150eu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
84150.er3	84150eu1	\([1, -1, 1, -46225805, 119759254197]\)	\(959024269496848362625/11151660319506432\)	\(127024380826877952000000\)	\([2]\)	\(13271040\)	\(3.2457\)	\(\Gamma_0(N)\)-optimal
84150.er4	84150eu2	\([1, -1, 1, -9361805, 305480086197]\)	\(-7966267523043306625/3534510366354604032\)	\(-40260282141757911552000000\)	\([2]\)	\(26542080\)	\(3.5922\)
84150.er1	84150eu3	\([1, -1, 1, -3733777805, 87816360598197]\)	\(505384091400037554067434625/815656731648\)	\(9290839958928000000\)	\([2]\)	\(39813120\)	\(3.7950\)
84150.er2	84150eu4	\([1, -1, 1, -3733741805, 87818138638197]\)	\(-505369473241574671219626625/20303219722982711328\)	\(-231266362157099946220500000\)	\([2]\)	\(79626240\)	\(4.1415\)

Rank

The elliptic curves in class 84150eu have rank \(1\).

Complex multiplication

The elliptic curves in class 84150eu do not have complex multiplication.

Modular form 84150.2.a.eu

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.