Elliptic curve isogeny class with Cremona label 444675ec (LMFDB label 444675.ec)

• Label: 444675ec
• Number of curves: $2$
• Conductor: $444675$
• CM: no
• Rank: $2$

Elliptic curves in class 444675ec

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
444675.ec2	444675ec1	\([0, 1, 1, -1086983, -134046181]\)	\(360448/189\)	\(74475178285239703125\)	\([]\)	\(10948608\)	\(2.5048\)	\(\Gamma_0(N)\)-optimal^*
444675.ec1	444675ec2	\([0, 1, 1, -50001233, 136067682944]\)	\(35084566528/1029\)	\(405475970664082828125\)	\([]\)	\(32845824\)	\(3.0541\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 444675ec1.

Rank

The elliptic curves in class 444675ec have rank \(2\).

Complex multiplication

The elliptic curves in class 444675ec do not have complex multiplication.

Modular form 444675.2.a.ec

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.