Elliptic curve isogeny class with Cremona label 1827e (LMFDB label 1827.e)

• Label: 1827e
• Number of curves: $2$
• Conductor: $1827$
• CM: no
• Rank: $0$

Elliptic curves in class 1827e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1827.e2	1827e1	\([0, 0, 1, 177, 31]\)	\(841232384/487403\)	\(-355316787\)	\([]\)	\(1440\)	\(0.33017\)	\(\Gamma_0(N)\)-optimal
1827.e1	1827e2	\([0, 0, 1, -19353, 1036381]\)	\(-1099616058781696/143578043\)	\(-104668393347\)	\([]\)	\(7200\)	\(1.1349\)

Rank

The elliptic curves in class 1827e have rank \(0\).

Complex multiplication

The elliptic curves in class 1827e do not have complex multiplication.

Modular form 1827.2.a.e

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.