Elliptic curve isogeny class with Cremona label 2178h (LMFDB label 2178.i)

• Label: 2178h
• Number of curves: $2$
• Conductor: $2178$
• CM: no
• Rank: $1$

Elliptic curves in class 2178h

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2178.i2	2178h1	\([1, -1, 1, -320, 1059]\)	\(3723875/1728\)	\(1676676672\)	\([2]\)	\(1152\)	\(0.46458\)	\(\Gamma_0(N)\)-optimal
2178.i1	2178h2	\([1, -1, 1, -4280, 108771]\)	\(8934171875/5832\)	\(5658783768\)	\([2]\)	\(2304\)	\(0.81115\)

Rank

The elliptic curves in class 2178h have rank \(1\).

Complex multiplication

The elliptic curves in class 2178h do not have complex multiplication.

Modular form 2178.2.a.h

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.