Elliptic curve isogeny class with LMFDB label 442090.b (Cremona label 442090b)

• Label: 442090.b
• Number of curves: $2$
• Conductor: $442090$
• CM: no
• Rank: $1$

Elliptic curves in class 442090.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
442090.b1	442090b2	\([1, -1, 1, -4225147137, -105870737945631]\)	\(-8341597385983597776317165707664481/14904201570185248149434970320\)	\(-14904201570185248149434970320\)	\([]\)	\(813189888\)	\(4.2986\)
442090.b2	442090b1	\([1, -1, 1, 3169263, 61621374849]\)	\(3520454064209678324329119/1642467221810708480000000\)	\(-1642467221810708480000000\)	\([7]\)	\(116169984\)	\(3.3256\)	\(\Gamma_0(N)\)-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 442090.b1.

Rank

The elliptic curves in class 442090.b have rank \(1\).

Complex multiplication

The elliptic curves in class 442090.b do not have complex multiplication.

Modular form 442090.2.a.b

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.