Elliptic curve isogeny class with LMFDB label 474075.cq (Cremona label 474075cq)

• Label: 474075.cq
• Number of curves: $2$
• Conductor: $474075$
• CM: no
• Rank: $1$

Elliptic curves in class 474075.cq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
474075.cq1	474075cq2	\([1, -1, 0, -1531253292, 23063535103741]\)	\(8000051600110940079507/144453125\)	\(7169666781005859375\)	\([2]\)	\(123863040\)	\(3.6089\)	\(\Gamma_0(N)\)-optimal^*
474075.cq2	474075cq1	\([1, -1, 0, -95706417, 360361275616]\)	\(1953326569433829507/262451171875\)	\(13026284122467041015625\)	\([2]\)	\(61931520\)	\(3.2623\)	\(\Gamma_0(N)\)-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 474075.cq1.

Rank

The elliptic curves in class 474075.cq have rank \(1\).

Complex multiplication

The elliptic curves in class 474075.cq do not have complex multiplication.

Modular form 474075.2.a.cq

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.