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

• Label: 425880.fb
• Number of curves: $6$
• Conductor: $425880$
• CM: no
• Rank: $1$

Elliptic curves in class 425880.fb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
425880.fb1	425880fb4	\([0, 0, 0, -10221627, -12578479706]\)	\(32779037733124/315\)	\(1135005987548160\)	\([2]\)	\(9437184\)	\(2.4671\)
425880.fb2	425880fb5	\([0, 0, 0, -9856587, 11870439334]\)	\(14695548366242/57421875\)	\(413804266293600000000\)	\([2]\)	\(18874368\)	\(2.8137\)	\(\Gamma_0(N)\)-optimal^*
425880.fb3	425880fb3	\([0, 0, 0, -913107, -11868194]\)	\(23366901604/13505625\)	\(48663381716127360000\)	\([2, 2]\)	\(9437184\)	\(2.4671\)	\(\Gamma_0(N)\)-optimal^*
425880.fb4	425880fb2	\([0, 0, 0, -639327, -196231646]\)	\(32082281296/99225\)	\(89381721519417600\)	\([2, 2]\)	\(4718592\)	\(2.1205\)	\(\Gamma_0(N)\)-optimal^*
425880.fb5	425880fb1	\([0, 0, 0, -23322, -5639699]\)	\(-24918016/229635\)	\(-12928427576915760\)	\([2]\)	\(2359296\)	\(1.7740\)	\(\Gamma_0(N)\)-optimal^*
425880.fb6	425880fb6	\([0, 0, 0, 3649893, -94914794]\)	\(746185003198/432360075\)	\(-3115754120011247769600\)	\([2]\)	\(18874368\)	\(2.8137\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 425880.fb1.

Rank

The elliptic curves in class 425880.fb have rank \(1\).

Complex multiplication

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

Modular form 425880.2.a.fb

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.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.