Elliptic curve isogeny class with Cremona label 473382fe (LMFDB label 473382.fe)

• Label: 473382fe
• Number of curves: $3$
• Conductor: $473382$
• CM: no
• Rank: $0$

Elliptic curves in class 473382fe

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
473382.fe3	473382fe1	\([1, -1, 1, 35059, -24035331]\)	\(270840023/14329224\)	\(-252141149468996424\)	\([]\)	\(8709120\)	\(2.0188\)	\(\Gamma_0(N)\)-optimal^*
473382.fe2	473382fe2	\([1, -1, 1, -316076, 655059759]\)	\(-198461344537/10417365504\)	\(-183306961536593416704\)	\([]\)	\(26127360\)	\(2.5681\)	\(\Gamma_0(N)\)-optimal^*
473382.fe1	473382fe3	\([1, -1, 1, -67773011, 214770472179]\)	\(-1956469094246217097/36641439744\)	\(-644753319178423762944\)	\([]\)	\(78382080\)	\(3.1174\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 473382fe1.

Rank

The elliptic curves in class 473382fe have rank \(0\).

Complex multiplication

The elliptic curves in class 473382fe do not have complex multiplication.

Modular form 473382.2.a.fe

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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.