Elliptic curve isogeny class with LMFDB label 117045.i (Cremona label 117045w)

• Label: 117045.i
• Number of curves: $2$
• Conductor: $117045$
• CM: no
• Rank: $0$

Elliptic curves in class 117045.i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
117045.i1	117045w2	\([1, -1, 1, -585713, 173425942]\)	\(-15590912409/78125\)	\(-111351508740703125\)	\([]\)	\(1241856\)	\(2.1183\)
117045.i2	117045w1	\([1, -1, 1, -488, -128384]\)	\(-9/5\)	\(-7126496559405\)	\([]\)	\(177408\)	\(1.1453\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 117045.i have rank \(0\).

Complex multiplication

The elliptic curves in class 117045.i do not have complex multiplication.

Modular form 117045.2.a.i

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.