Elliptic curve isogeny class with LMFDB label 447174.by (Cremona label 447174by)

• Label: 447174.by
• Number of curves: $3$
• Conductor: $447174$
• CM: no
• Rank: $0$

Elliptic curves in class 447174.by

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
447174.by1	447174by3	\([1, -1, 0, -79163772, 271124988434]\)	\(-545407363875/14\)	\(-1408348681478298378\)	\([]\)	\(31912704\)	\(2.9986\)	\(\Gamma_0(N)\)-optimal^*
447174.by2	447174by2	\([1, -1, 0, -908322, 426866012]\)	\(-7414875/2744\)	\(-30670704618860720232\)	\([]\)	\(10637568\)	\(2.4493\)	\(\Gamma_0(N)\)-optimal^*
447174.by3	447174by1	\([1, -1, 0, 85398, -5932172]\)	\(4492125/3584\)	\(-54951571781503488\)	\([]\)	\(3545856\)	\(1.9000\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 447174.by1.

Rank

The elliptic curves in class 447174.by have rank \(0\).

Complex multiplication

The elliptic curves in class 447174.by do not have complex multiplication.

Modular form 447174.2.a.by

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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.