Elliptic curve isogeny class with LMFDB label 411840.dm (Cremona label 411840dm)

• Label: 411840.dm
• Number of curves: $4$
• Conductor: $411840$
• CM: no
• Rank: $2$

Elliptic curves in class 411840.dm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
411840.dm1	411840dm4	\([0, 0, 0, -92405388, -341887912688]\)	\(456612868287073618849/12544848030000\)	\(2397357792000737280000\)	\([2]\)	\(37748736\)	\(3.2058\)
411840.dm2	411840dm3	\([0, 0, 0, -25773708, 45531677968]\)	\(9908022260084596129/1047363281250000\)	\(200154240000000000000000\)	\([2]\)	\(37748736\)	\(3.2058\)	\(\Gamma_0(N)\)-optimal^*
411840.dm3	411840dm2	\([0, 0, 0, -6005388, -4893352688]\)	\(125337052492018849/18404100000000\)	\(3517078280601600000000\)	\([2, 2]\)	\(18874368\)	\(2.8592\)	\(\Gamma_0(N)\)-optimal^*
411840.dm4	411840dm1	\([0, 0, 0, 630132, -415703792]\)	\(144794100308831/474439680000\)	\(-90666834780487680000\)	\([2]\)	\(9437184\)	\(2.5126\)	\(\Gamma_0(N)\)-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 411840.dm1.

Rank

The elliptic curves in class 411840.dm have rank \(2\).

Complex multiplication

The elliptic curves in class 411840.dm do not have complex multiplication.

Modular form 411840.2.a.dm

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.