Elliptic curve isogeny class with LMFDB label 442225.cc (Cremona label 442225cc)

• Label: 442225.cc
• Number of curves: $2$
• Conductor: $442225$
• CM: no
• Rank: $1$

Elliptic curves in class 442225.cc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
442225.cc1	442225cc2	\([1, 1, 0, -3680780555, -85953932640050]\)	\(-162677523113838677\)	\(-33901267729335125\)	\([]\)	\(81454464\)	\(3.7157\)
442225.cc2	442225cc1	\([1, 1, 0, -141880, 22337225]\)	\(-9317\)	\(-33901267729335125\)	\([]\)	\(2201472\)	\(1.9102\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 442225.cc1.

Rank

The elliptic curves in class 442225.cc have rank \(1\).

Complex multiplication

The elliptic curves in class 442225.cc do not have complex multiplication.

Modular form 442225.2.a.cc

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.

\(\left(\begin{array}{rr} 1 & 37 \\ 37 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.