Elliptic curve isogeny class with Cremona label 425880n (LMFDB label 425880.n)

• Label: 425880n
• Number of curves: $4$
• Conductor: $425880$
• CM: no
• Rank: $0$

Elliptic curves in class 425880n

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
425880.n4	425880n1	\([0, 0, 0, 33462, 1364337]\)	\(73598976/56875\)	\(-3202056822510000\)	\([2]\)	\(2064384\)	\(1.6633\)	\(\Gamma_0(N)\)-optimal^*
425880.n3	425880n2	\([0, 0, 0, -156663, 11745162]\)	\(472058064/207025\)	\(186487789342982400\)	\([2, 2]\)	\(4128768\)	\(2.0098\)	\(\Gamma_0(N)\)-optimal^*
425880.n1	425880n3	\([0, 0, 0, -2133963, 1199311542]\)	\(298261205316/156065\)	\(562332410941916160\)	\([2]\)	\(8257536\)	\(2.3564\)	\(\Gamma_0(N)\)-optimal^*
425880.n2	425880n4	\([0, 0, 0, -1221363, -511448418]\)	\(55920415716/999635\)	\(3601878445595888640\)	\([2]\)	\(8257536\)	\(2.3564\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 425880n1.

Rank

The elliptic curves in class 425880n have rank \(0\).

Complex multiplication

The elliptic curves in class 425880n do not have complex multiplication.

Modular form 425880.2.a.n

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.