Elliptic curve isogeny class with LMFDB label 431200.fb (Cremona label 431200fb)

• Label: 431200.fb
• Number of curves: $2$
• Conductor: $431200$
• CM: no
• Rank: $1$

Elliptic curves in class 431200.fb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
431200.fb1	431200fb2	\([0, -1, 0, -5176033, 4322813937]\)	\(2036792051776/107421875\)	\(808836875000000000000\)	\([2]\)	\(17694720\)	\(2.7688\)
431200.fb2	431200fb1	\([0, -1, 0, -5108658, 4446042812]\)	\(125330290485184/378125\)	\(44486028125000000\)	\([2]\)	\(8847360\)	\(2.4222\)	\(\Gamma_0(N)\)-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 431200.fb1.

Rank

The elliptic curves in class 431200.fb have rank \(1\).

Complex multiplication

The elliptic curves in class 431200.fb do not have complex multiplication.

Modular form 431200.2.a.fb

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.