Elliptic curve isogeny class with LMFDB label 12789.i (Cremona label 12789n)

• Label: 12789.i
• Number of curves: $2$
• Conductor: $12789$
• CM: no
• Rank: $2$

Elliptic curves in class 12789.i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
12789.i1	12789n2	\([0, 0, 1, -714, -7205]\)	\(1126924288/24389\)	\(871199469\)	\([]\)	\(6048\)	\(0.50400\)
12789.i2	12789n1	\([0, 0, 1, -84, 292]\)	\(1835008/29\)	\(1035909\)	\([]\)	\(2016\)	\(-0.045308\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 12789.i have rank \(2\).

Complex multiplication

The elliptic curves in class 12789.i do not have complex multiplication.

Modular form 12789.2.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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.