Elliptic curve isogeny class with LMFDB label 478800.ef (Cremona label 478800ef)

• Label: 478800.ef
• Number of curves: $4$
• Conductor: $478800$
• CM: no
• Rank: $0$

Elliptic curves in class 478800.ef

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
478800.ef1	478800ef3	\([0, 0, 0, -320175075, 2128031937250]\)	\(77799851782095807001/3092322318750000\)	\(144275390103600000000000000\)	\([2]\)	\(113246208\)	\(3.7861\)	\(\Gamma_0(N)\)-optimal^*
478800.ef2	478800ef2	\([0, 0, 0, -52047075, -99843614750]\)	\(334199035754662681/101099003040000\)	\(4716875085834240000000000\)	\([2, 2]\)	\(56623104\)	\(3.4395\)	\(\Gamma_0(N)\)-optimal^*
478800.ef3	478800ef1	\([0, 0, 0, -47439075, -125745182750]\)	\(253060782505556761/41184460800\)	\(1921502203084800000000\)	\([2]\)	\(28311552\)	\(3.0930\)	\(\Gamma_0(N)\)-optimal^*
478800.ef4	478800ef4	\([0, 0, 0, 142352925, -670018814750]\)	\(6837784281928633319/8113766016106800\)	\(-378555867247478860800000000\)	\([2]\)	\(113246208\)	\(3.7861\)

^*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 478800.ef1.

Rank

The elliptic curves in class 478800.ef have rank \(0\).

Complex multiplication

The elliptic curves in class 478800.ef do not have complex multiplication.

Modular form 478800.2.a.ef

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.