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

• Label: 418950qf
• Number of curves: $2$
• Conductor: $418950$
• CM: no
• Rank: $0$

Elliptic curves in class 418950qf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
418950.qf2	418950qf1	\([1, -1, 1, -16052630, -24864857503]\)	\(-341370886042369/1817528220\)	\(-2435661644334915937500\)	\([2]\)	\(38707200\)	\(2.9485\)	\(\Gamma_0(N)\)-optimal^*
418950.qf1	418950qf2	\([1, -1, 1, -257169380, -1587301397503]\)	\(1403607530712116449/39475350\)	\(52900744447146093750\)	\([2]\)	\(77414400\)	\(3.2951\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 418950qf1.

Rank

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

Complex multiplication

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

Modular form 418950.2.a.qf

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.