Elliptic curve isogeny class with LMFDB label 272.b (Cremona label 272b)

• Label: 272.b
• Number of curves: $4$
• Conductor: $272$
• CM: no
• Rank: $1$

Elliptic curves in class 272.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
272.b1	272b3	\([0, 0, 0, -1451, 21274]\)	\(82483294977/17\)	\(69632\)	\([4]\)	\(64\)	\(0.31651\)
272.b2	272b2	\([0, 0, 0, -91, 330]\)	\(20346417/289\)	\(1183744\)	\([2, 2]\)	\(32\)	\(-0.030063\)
272.b3	272b1	\([0, 0, 0, -11, -6]\)	\(35937/17\)	\(69632\)	\([2]\)	\(16\)	\(-0.37664\)	\(\Gamma_0(N)\)-optimal
272.b4	272b4	\([0, 0, 0, -11, 890]\)	\(-35937/83521\)	\(-342102016\)	\([4]\)	\(64\)	\(0.31651\)

Rank

The elliptic curves in class 272.b have rank \(1\).

Complex multiplication

The elliptic curves in class 272.b do not have complex multiplication.

Modular form 272.2.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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.