Elliptic curve isogeny class with Cremona label 418950dy (LMFDB label 418950.dy)

• Label: 418950dy
• Number of curves: $4$
• Conductor: $418950$
• CM: no
• Rank: $0$

Elliptic curves in class 418950dy

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
418950.dy3	418950dy1	\([1, -1, 0, -145282167, -673879268259]\)	\(253060782505556761/41184460800\)	\(55191116379571200000000\)	\([2]\)	\(56623104\)	\(3.3728\)	\(\Gamma_0(N)\)-optimal^*
418950.dy2	418950dy2	\([1, -1, 0, -159394167, -535059524259]\)	\(334199035754662681/101099003040000\)	\(135482333245437622500000000\)	\([2, 2]\)	\(113246208\)	\(3.7193\)	\(\Gamma_0(N)\)-optimal^*
418950.dy1	418950dy3	\([1, -1, 0, -980536167, 11405166297741]\)	\(77799851782095807001/3092322318750000\)	\(4144007658764266699218750000\)	\([2]\)	\(226492416\)	\(4.0659\)	\(\Gamma_0(N)\)-optimal^*
418950.dy4	418950dy4	\([1, -1, 0, 435955833, -3590991074259]\)	\(6837784281928633319/8113766016106800\)	\(-10873222467235996214418750000\)	\([2]\)	\(226492416\)	\(4.0659\)

^*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 418950dy1.

Rank

The elliptic curves in class 418950dy have rank \(0\).

Complex multiplication

The elliptic curves in class 418950dy do not have complex multiplication.

Modular form 418950.2.a.dy

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.