Elliptic curve isogeny class with LMFDB label 67830.r (Cremona label 67830q)

• Label: 67830.r
• Number of curves: $4$
• Conductor: $67830$
• CM: no
• Rank: $1$

Elliptic curves in class 67830.r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
67830.r1	67830q4	\([1, 0, 1, -31034, 2101646]\)	\(3305345506018293529/8724633750\)	\(8724633750\)	\([2]\)	\(147456\)	\(1.1429\)
67830.r2	67830q2	\([1, 0, 1, -1964, 31862]\)	\(837201991720249/41408180100\)	\(41408180100\)	\([2, 2]\)	\(73728\)	\(0.79635\)
67830.r3	67830q1	\([1, 0, 1, -344, -1834]\)	\(4483146738169/1186753680\)	\(1186753680\)	\([2]\)	\(36864\)	\(0.44978\)	\(\Gamma_0(N)\)-optimal
67830.r4	67830q3	\([1, 0, 1, 1186, 125102]\)	\(184715807453351/6857260351830\)	\(-6857260351830\)	\([2]\)	\(147456\)	\(1.1429\)

Rank

The elliptic curves in class 67830.r have rank \(1\).

Complex multiplication

The elliptic curves in class 67830.r do not have complex multiplication.

Modular form 67830.2.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.