Properties

Label 257600.y
Number of curves $2$
Conductor $257600$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("y1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 257600.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
257600.y1 257600y2 \([0, 1, 0, -48833, -4169537]\) \(12576878500/1127\) \(1154048000000\) \([2]\) \(737280\) \(1.3545\)  
257600.y2 257600y1 \([0, 1, 0, -2833, -75537]\) \(-9826000/3703\) \(-947968000000\) \([2]\) \(368640\) \(1.0080\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 257600.y have rank \(1\).

Complex multiplication

The elliptic curves in class 257600.y do not have complex multiplication.

Modular form 257600.2.a.y

sage: E.q_eigenform(10)
 
\(q - 2q^{3} - q^{7} + q^{9} + 4q^{11} + 6q^{13} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.