Elliptic curve isogeny class with LMFDB label 412200.g (Cremona label 412200g)

• Label: 412200.g
• Number of curves: $2$
• Conductor: $412200$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 412200.g have rank \(1\).

Complex multiplication

The elliptic curves in class 412200.g do not have complex multiplication.

Modular form 412200.2.a.g

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.

Elliptic curves in class 412200.g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
412200.g1	412200g2	\([0, 0, 0, -846075, 138919750]\)	\(5742523604164/2608453125\)	\(30424997250000000000\)	\([2]\)	\(9732096\)	\(2.4336\)	\(\Gamma_0(N)\)-optimal^*
412200.g2	412200g1	\([0, 0, 0, 184425, 16290250]\)	\(237900617264/176988375\)	\(-516098101500000000\)	\([2]\)	\(4866048\)	\(2.0870\)	\(\Gamma_0(N)\)-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 412200.g1.