Elliptic curve isogeny class with Cremona label 454860bh (LMFDB label 454860.bh)

• Label: 454860bh
• Number of curves: $2$
• Conductor: $454860$
• CM: no
• Rank: $0$

Elliptic curves in class 454860bh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
454860.bh2	454860bh1	\([0, 0, 0, -4332, -61731]\)	\(442368/175\)	\(3556668603600\)	\([2]\)	\(628992\)	\(1.1067\)	\(\Gamma_0(N)\)-optimal^*
454860.bh1	454860bh2	\([0, 0, 0, -31407, 2098854]\)	\(10536048/245\)	\(79669376720640\)	\([2]\)	\(1257984\)	\(1.4533\)	\(\Gamma_0(N)\)-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 454860bh1.

Rank

The elliptic curves in class 454860bh have rank \(0\).

Complex multiplication

The elliptic curves in class 454860bh do not have complex multiplication.

Modular form 454860.2.a.bh

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.