Elliptic curve isogeny class with Cremona label 38a (LMFDB label 38.a)

• Label: 38a
• Number of curves: $3$
• Conductor: $38$
• CM: no
• Rank: $0$

Elliptic curves in class 38a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
38.a3	38a1	\([1, 0, 1, 9, 90]\)	\(94196375/3511808\)	\(-3511808\)	\([3]\)	\(6\)	\(-0.064137\)	\(\Gamma_0(N)\)-optimal
38.a1	38a2	\([1, 0, 1, -86, -2456]\)	\(-69173457625/2550136832\)	\(-2550136832\)	\([]\)	\(18\)	\(0.48517\)
38.a2	38a3	\([1, 0, 1, -16, 22]\)	\(-413493625/152\)	\(-152\)	\([3]\)	\(18\)	\(-0.61344\)

Rank

The elliptic curves in class 38a have rank \(0\).

Complex multiplication

The elliptic curves in class 38a do not have complex multiplication.

Modular form 38.2.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 Cremona numbering.

\(\left(\begin{array}{rrr} 1 & 3 & 3 \\ 3 & 1 & 9 \\ 3 & 9 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.