Elliptic curve isogeny class with LMFDB label 457200.dt (Cremona label 457200dt)

• Label: 457200.dt
• Number of curves: $2$
• Conductor: $457200$
• CM: no
• Rank: $0$

Elliptic curves in class 457200.dt

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
457200.dt1	457200dt2	\([0, 0, 0, -80499981675, -8791070728859750]\)	\(1236526859255318155975783969/38367061931916216\)	\(1790053641495482973696000000\)	\([]\)	\(695439360\)	\(4.7336\)
457200.dt2	457200dt1	\([0, 0, 0, -367005675, 2680643700250]\)	\(117174888570509216929/1273887851544576\)	\(59434511601663737856000000\)	\([]\)	\(99348480\)	\(3.7607\)	\(\Gamma_0(N)\)-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 457200.dt1.

Rank

The elliptic curves in class 457200.dt have rank \(0\).

Complex multiplication

The elliptic curves in class 457200.dt do not have complex multiplication.

Modular form 457200.2.a.dt

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.