Elliptic curve isogeny class with Cremona label 325325t (LMFDB label 325325.t)

• Label: 325325t
• Number of curves: $4$
• Conductor: $325325$
• CM: no
• Rank: $1$

Elliptic curves in class 325325t

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
325325.t4	325325t1	\([1, -1, 1, -66280, -55363278]\)	\(-426957777/17320303\)	\(-1306278037548859375\)	\([2]\)	\(3268608\)	\(2.1563\)	\(\Gamma_0(N)\)-optimal
325325.t3	325325t2	\([1, -1, 1, -2622405, -1624824028]\)	\(26444947540257/169338169\)	\(12771296846448765625\)	\([2, 2]\)	\(6537216\)	\(2.5028\)
325325.t2	325325t3	\([1, -1, 1, -4249030, 632931472]\)	\(112489728522417/62811265517\)	\(4737155964044457078125\)	\([2]\)	\(13074432\)	\(2.8494\)
325325.t1	325325t4	\([1, -1, 1, -41893780, -104358741028]\)	\(107818231938348177/4463459\)	\(336629126130171875\)	\([2]\)	\(13074432\)	\(2.8494\)

Rank

The elliptic curves in class 325325t have rank \(1\).

Complex multiplication

The elliptic curves in class 325325t do not have complex multiplication.

Modular form 325325.2.a.t

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.