Elliptic curve isogeny class with Cremona label 475b (LMFDB label 475.c)

• Label: 475b
• Number of curves: $2$
• Conductor: $475$
• CM: no
• Rank: $1$

Elliptic curves in class 475b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
475.c2	475b1	\([1, -1, 0, 8, 291]\)	\(27/19\)	\(-37109375\)	\([2]\)	\(80\)	\(0.13149\)	\(\Gamma_0(N)\)-optimal
475.c1	475b2	\([1, -1, 0, -617, 5916]\)	\(13312053/361\)	\(705078125\)	\([2]\)	\(160\)	\(0.47806\)

Rank

The elliptic curves in class 475b have rank \(1\).

Complex multiplication

The elliptic curves in class 475b do not have complex multiplication.

Modular form 475.2.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 Cremona numbering.

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

Isogeny graph

The vertices are labelled with Cremona labels.