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

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

Elliptic curves in class 452400m

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
452400.m3	452400m1	\([0, -1, 0, -709008, -229543488]\)	\(615882348586441/21715200\)	\(1389772800000000\)	\([2]\)	\(7077888\)	\(1.9955\)	\(\Gamma_0(N)\)-optimal^*
452400.m2	452400m2	\([0, -1, 0, -741008, -207655488]\)	\(703093388853961/115124490000\)	\(7367967360000000000\)	\([2, 2]\)	\(14155776\)	\(2.3420\)	\(\Gamma_0(N)\)-optimal^*
452400.m1	452400m3	\([0, -1, 0, -3341008, 2153144512]\)	\(64443098670429961/6032611833300\)	\(386087157331200000000\)	\([2]\)	\(28311552\)	\(2.6886\)	\(\Gamma_0(N)\)-optimal^*
452400.m4	452400m4	\([0, -1, 0, 1346992, -1168135488]\)	\(4223169036960119/11647532812500\)	\(-745442100000000000000\)	\([2]\)	\(28311552\)	\(2.6886\)

^*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 452400m1.

Rank

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

Complex multiplication

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

Modular form 452400.2.a.m

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.