Elliptic curve isogeny class with Cremona label 137275q (LMFDB label 137275.q)

• Label: 137275q
• Number of curves: $2$
• Conductor: $137275$
• CM: no
• Rank: $1$

Elliptic curves in class 137275q

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
137275.q2	137275q1	\([1, -1, 0, 2258, 1438791]\)	\(27/19\)	\(-895730099609375\)	\([2]\)	\(394240\)	\(1.5481\)	\(\Gamma_0(N)\)-optimal
137275.q1	137275q2	\([1, -1, 0, -178367, 28351916]\)	\(13312053/361\)	\(17018871892578125\)	\([2]\)	\(788480\)	\(1.8947\)

Rank

The elliptic curves in class 137275q have rank \(1\).

Complex multiplication

The elliptic curves in class 137275q do not have complex multiplication.

Modular form 137275.2.a.q

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 Cremona numbering.

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

Isogeny graph

The vertices are labelled with Cremona labels.