Elliptic curve isogeny class with LMFDB label 72.a (Cremona label 72a)

• Label: 72.a
• Number of curves: $6$
• Conductor: $72$
• CM: no
• Rank: $0$

Elliptic curves in class 72.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
72.a1	72a5	\([0, 0, 0, -3459, 78302]\)	\(3065617154/9\)	\(13436928\)	\([2]\)	\(32\)	\(0.59710\)
72.a2	72a3	\([0, 0, 0, -579, -5362]\)	\(28756228/3\)	\(2239488\)	\([2]\)	\(16\)	\(0.25053\)
72.a3	72a4	\([0, 0, 0, -219, 1190]\)	\(1556068/81\)	\(60466176\)	\([2, 2]\)	\(16\)	\(0.25053\)
72.a4	72a2	\([0, 0, 0, -39, -70]\)	\(35152/9\)	\(1679616\)	\([2, 2]\)	\(8\)	\(-0.096046\)
72.a5	72a1	\([0, 0, 0, 6, -7]\)	\(2048/3\)	\(-34992\)	\([4]\)	\(4\)	\(-0.44262\)	\(\Gamma_0(N)\)-optimal
72.a6	72a6	\([0, 0, 0, 141, 4718]\)	\(207646/6561\)	\(-9795520512\)	\([2]\)	\(32\)	\(0.59710\)

Rank

The elliptic curves in class 72.a have rank \(0\).

Complex multiplication

The elliptic curves in class 72.a do not have complex multiplication.

Modular form 72.2.a.a

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.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.