Properties

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

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 256025.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
256025.q1 256025q1 \([0, 1, 1, -33483, -2769056]\) \(-2258403328/480491\) \(-883270088421875\) \([]\) \(746496\) \(1.5893\) \(\Gamma_0(N)\)-optimal
256025.q2 256025q2 \([0, 1, 1, 236017, 16028569]\) \(790939860992/517504691\) \(-951311084241546875\) \([]\) \(2239488\) \(2.1386\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 256025.2.a.q

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{4} - 2 q^{9} + q^{11} - 2 q^{12} + 2 q^{13} + 4 q^{16} - q^{19} + O(q^{20})\) 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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.