Elliptic curve isogeny class with Cremona label 17325q (LMFDB label 17325.bi)

• Label: 17325q
• Number of curves: $4$
• Conductor: $17325$
• CM: no
• Rank: $1$

Elliptic curves in class 17325q

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
17325.bi3	17325q1	\([1, -1, 0, -3654567, 2689983216]\)	\(473897054735271721/779625\)	\(8880416015625\)	\([2]\)	\(221184\)	\(2.1764\)	\(\Gamma_0(N)\)-optimal
17325.bi2	17325q2	\([1, -1, 0, -3655692, 2688245091]\)	\(474334834335054841/607815140625\)	\(6923394336181640625\)	\([2, 2]\)	\(442368\)	\(2.5229\)
17325.bi1	17325q3	\([1, -1, 0, -4658067, 1097475966]\)	\(981281029968144361/522287841796875\)	\(5949184947967529296875\)	\([2]\)	\(884736\)	\(2.8695\)
17325.bi4	17325q4	\([1, -1, 0, -2671317, 4167760716]\)	\(-185077034913624841/551466161890875\)	\(-6281544250288248046875\)	\([2]\)	\(884736\)	\(2.8695\)

Rank

The elliptic curves in class 17325q have rank \(1\).

Complex multiplication

The elliptic curves in class 17325q do not have complex multiplication.

Modular form 17325.2.a.q

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.