Elliptic curve isogeny class with Cremona label 27380c (LMFDB label 27380.e)

• Label: 27380c
• Number of curves: $2$
• Conductor: $27380$
• CM: no
• Rank: $1$

Elliptic curves in class 27380c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
27380.e2	27380c1	\([0, 1, 0, -248245, -18550457]\)	\(2575826944/1266325\)	\(831755134688492800\)	\([]\)	\(196992\)	\(2.1317\)	\(\Gamma_0(N)\)-optimal
27380.e1	27380c2	\([0, 1, 0, -16457205, -25702458025]\)	\(750484394082304/578125\)	\(379727508532000000\)	\([]\)	\(590976\)	\(2.6810\)

Rank

The elliptic curves in class 27380c have rank \(1\).

Complex multiplication

The elliptic curves in class 27380c do not have complex multiplication.

Modular form 27380.2.a.c

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.