Elliptic curve isogeny class with Cremona label 436425cd (LMFDB label 436425.cd)

• Label: 436425cd
• Number of curves: $2$
• Conductor: $436425$
• CM: no
• Rank: $1$

Elliptic curves in class 436425cd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
436425.cd2	436425cd1	\([1, 0, 1, -304451, 940225673]\)	\(-1349232625/164333367\)	\(-380113063690754109375\)	\([2]\)	\(12165120\)	\(2.6284\)	\(\Gamma_0(N)\)-optimal^*
436425.cd1	436425cd2	\([1, 0, 1, -16372826, 25299882173]\)	\(209849322390625/1882056627\)	\(4353311342598225046875\)	\([2]\)	\(24330240\)	\(2.9750\)	\(\Gamma_0(N)\)-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 436425cd1.

Rank

The elliptic curves in class 436425cd have rank \(1\).

Complex multiplication

The elliptic curves in class 436425cd do not have complex multiplication.

Modular form 436425.2.a.cd

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.