Elliptic curve isogeny class with Cremona label 394944by (LMFDB label 394944.by)

• Label: 394944by
• Number of curves: $4$
• Conductor: $394944$
• CM: no
• Rank: $1$

Elliptic curves in class 394944by

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
394944.by3	394944by1	\([0, -1, 0, -1590989473, 24179701612321]\)	\(959024269496848362625/11151660319506432\)	\(5178876626805754214574194688\)	\([2]\)	\(265420800\)	\(4.1303\)	\(\Gamma_0(N)\)-optimal
394944.by4	394944by2	\([0, -1, 0, -322212513, 61681449729825]\)	\(-7966267523043306625/3534510366354604032\)	\(-1641441058915491164594884313088\)	\([2]\)	\(530841600\)	\(4.4769\)
394944.by1	394944by3	\([0, -1, 0, -128508334753, 17731525731909409]\)	\(505384091400037554067434625/815656731648\)	\(378794319590211591340032\)	\([2]\)	\(796262400\)	\(4.6796\)
394944.by2	394944by4	\([0, -1, 0, -128507095713, 17731884750935841]\)	\(-505369473241574671219626625/20303219722982711328\)	\(-9428898214226683510900131889152\)	\([2]\)	\(1592524800\)	\(5.0262\)

Rank

The elliptic curves in class 394944by have rank \(1\).

Complex multiplication

The elliptic curves in class 394944by do not have complex multiplication.

Modular form 394944.2.a.by

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.