Elliptic curve isogeny class with LMFDB label 417600.jx (Cremona label 417600jx)

• Label: 417600.jx
• Number of curves: $2$
• Conductor: $417600$
• CM: no
• Rank: $0$

Elliptic curves in class 417600.jx

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
417600.jx1	417600jx2	\([0, 0, 0, -93758700, -350456398000]\)	\(-30526075007211889/103499257854\)	\(-309047127963918336000000\)	\([]\)	\(42147840\)	\(3.3714\)
417600.jx2	417600jx1	\([0, 0, 0, -14700, 236882000]\)	\(-117649/8118144\)	\(-24240648093696000000\)	\([]\)	\(6021120\)	\(2.3984\)	\(\Gamma_0(N)\)-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 417600.jx1.

Rank

The elliptic curves in class 417600.jx have rank \(0\).

Complex multiplication

The elliptic curves in class 417600.jx do not have complex multiplication.

Modular form 417600.2.a.jx

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.