Elliptic curve isogeny class with Cremona label 2700b (LMFDB label 2700.k)

• Label: 2700b
• Number of curves: $2$
• Conductor: $2700$
• CM: no
• Rank: $0$

Elliptic curves in class 2700b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2700.k1	2700b1	\([0, 0, 0, -16200, 796500]\)	\(-5971968/25\)	\(-1968300000000\)	\([]\)	\(5184\)	\(1.2140\)	\(\Gamma_0(N)\)-optimal
2700.k2	2700b2	\([0, 0, 0, 37800, 4198500]\)	\(8429568/15625\)	\(-11071687500000000\)	\([]\)	\(15552\)	\(1.7633\)

Rank

The elliptic curves in class 2700b have rank \(0\).

Complex multiplication

The elliptic curves in class 2700b do not have complex multiplication.

Modular form 2700.2.a.b

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.