Elliptic curve isogeny class with LMFDB label 49011.b (Cremona label 49011a)

• Label: 49011.b
• Number of curves: $2$
• Conductor: $49011$
• CM: no
• Rank: $1$

Elliptic curves in class 49011.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
49011.b1	49011a2	\([0, -1, 1, -57019, 5262498]\)	\(-23100424192/14739\)	\(-13080916754259\)	\([]\)	\(183600\)	\(1.4578\)
49011.b2	49011a1	\([0, -1, 1, 641, 29853]\)	\(32768/459\)	\(-407364189579\)	\([]\)	\(61200\)	\(0.90846\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 49011.b have rank \(1\).

Complex multiplication

The elliptic curves in class 49011.b do not have complex multiplication.

Modular form 49011.2.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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.