Elliptic curve isogeny class with LMFDB label 4017.b (Cremona label 4017c)

• Label: 4017.b
• Number of curves: $2$
• Conductor: $4017$
• CM: no
• Rank: $1$

Elliptic curves in class 4017.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
4017.b1	4017c2	\([1, 0, 0, -412, -103]\)	\(7735372650433/4474451943\)	\(4474451943\)	\([2]\)	\(2016\)	\(0.54128\)
4017.b2	4017c1	\([1, 0, 0, 103, 0]\)	\(120773549807/69923919\)	\(-69923919\)	\([2]\)	\(1008\)	\(0.19471\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 4017.b have rank \(1\).

Complex multiplication

The elliptic curves in class 4017.b do not have complex multiplication.

Modular form 4017.2.a.b

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.