Elliptic curve isogeny class with LMFDB label 540.b (Cremona label 540c)

• Label: 540.b
• Number of curves: $2$
• Conductor: $540$
• CM: no
• Rank: $1$

Elliptic curves in class 540.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
540.b1	540c1	\([0, 0, 0, -648, 6372]\)	\(-5971968/25\)	\(-125971200\)	\([3]\)	\(216\)	\(0.40927\)	\(\Gamma_0(N)\)-optimal
540.b2	540c2	\([0, 0, 0, 1512, 33588]\)	\(8429568/15625\)	\(-708588000000\)	\([]\)	\(648\)	\(0.95857\)

Rank

The elliptic curves in class 540.b have rank \(1\).

Complex multiplication

The elliptic curves in class 540.b do not have complex multiplication.

Modular form 540.2.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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.