Elliptic curve isogeny class with Cremona label 452400em (LMFDB label 452400.em)

• Label: 452400em
• Number of curves: $4$
• Conductor: $452400$
• CM: no
• Rank: $1$

Elliptic curves in class 452400em

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
452400.em4	452400em1	\([0, 1, 0, -11326008, -4208388012]\)	\(2510581756496128561/1333551278592000\)	\(85347281829888000000000\)	\([2]\)	\(39813120\)	\(3.0915\)	\(\Gamma_0(N)\)-optimal^*
452400.em2	452400em2	\([0, 1, 0, -104638008, 408790523988]\)	\(1979758117698975186481/17510434929000000\)	\(1120667835456000000000000\)	\([2, 2]\)	\(79626240\)	\(3.4381\)	\(\Gamma_0(N)\)-optimal^*
452400.em1	452400em3	\([0, 1, 0, -1670638008, 26282242523988]\)	\(8057323694463985606146481/638717154543000\)	\(40877897890752000000000\)	\([2]\)	\(159252480\)	\(3.7847\)	\(\Gamma_0(N)\)-optimal^*
452400.em3	452400em4	\([0, 1, 0, -31630008, 968761883988]\)	\(-54681655838565466801/6303365630859375000\)	\(-403415400375000000000000000\)	\([2]\)	\(159252480\)	\(3.7847\)

^*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 452400em1.

Rank

The elliptic curves in class 452400em have rank \(1\).

Complex multiplication

The elliptic curves in class 452400em do not have complex multiplication.

Modular form 452400.2.a.em

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.