Elliptic curve isogeny class with LMFDB label 38640.r (Cremona label 38640bo)

• Label: 38640.r
• Number of curves: $4$
• Conductor: $38640$
• CM: no
• Rank: $1$

Elliptic curves in class 38640.r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
38640.r1	38640bo4	\([0, -1, 0, -29496, -1810704]\)	\(692895692874169/51420783750\)	\(210619530240000\)	\([2]\)	\(147456\)	\(1.4942\)
38640.r2	38640bo2	\([0, -1, 0, -5976, 146160]\)	\(5763259856089/1143116100\)	\(4682203545600\)	\([2, 2]\)	\(73728\)	\(1.1476\)
38640.r3	38640bo1	\([0, -1, 0, -5656, 165616]\)	\(4886171981209/270480\)	\(1107886080\)	\([2]\)	\(36864\)	\(0.80100\)	\(\Gamma_0(N)\)-optimal
38640.r4	38640bo3	\([0, -1, 0, 12424, 852720]\)	\(51774168853511/107398242630\)	\(-439903201812480\)	\([2]\)	\(147456\)	\(1.4942\)

Rank

The elliptic curves in class 38640.r have rank \(1\).

Complex multiplication

The elliptic curves in class 38640.r do not have complex multiplication.

Modular form 38640.2.a.r

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.