↑

Properties

Label 256025x
Number of curves $2$
Conductor $256025$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 256025x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
256025.x2 256025x1 \([1, 0, 1, -7376, 192273]\) \(24137569/5225\) \(9604937890625\) \([2]\) \(552960\) \(1.2051\) \(\Gamma_0(N)\)-optimal
256025.x1 256025x2 \([1, 0, 1, -38001, -2686477]\) \(3301293169/218405\) \(401486403828125\) \([2]\) \(1105920\) \(1.5516\)  

Rank

sage: E.rank()
 

The elliptic curves in class 256025x have rank \(1\).

Complex multiplication

The elliptic curves in class 256025x do not have complex multiplication.

Modular form 256025.2.a.x

sage: E.q_eigenform(10)
 
\(q + q^{2} - 2 q^{3} - q^{4} - 2 q^{6} - 3 q^{8} + q^{9} - q^{11} + 2 q^{12} + 6 q^{13} - q^{16} + q^{18} + q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().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

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.