Elliptic curve isogeny class with Cremona label 27456by (LMFDB label 27456.by)

• Label: 27456by
• Number of curves: $4$
• Conductor: $27456$
• CM: no
• Rank: $1$

Elliptic curves in class 27456by

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
27456.by4	27456by1	\([0, 1, 0, 23007, -958113]\)	\(5137417856375/4510142208\)	\(-1182306718973952\)	\([2]\)	\(110592\)	\(1.5797\)	\(\Gamma_0(N)\)-optimal
27456.by3	27456by2	\([0, 1, 0, -115233, -8616609]\)	\(645532578015625/252306960048\)	\(66140755734822912\)	\([2]\)	\(221184\)	\(1.9262\)
27456.by2	27456by3	\([0, 1, 0, -239073, 60001695]\)	\(-5764706497797625/2612665516032\)	\(-684894589034692608\)	\([2]\)	\(331776\)	\(2.1290\)
27456.by1	27456by4	\([0, 1, 0, -4171233, 3277295007]\)	\(30618029936661765625/3678951124992\)	\(964414963709902848\)	\([2]\)	\(663552\)	\(2.4755\)

Rank

The elliptic curves in class 27456by have rank \(1\).

Complex multiplication

The elliptic curves in class 27456by do not have complex multiplication.

Modular form 27456.2.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.