Properties

Label 257600.u
Number of curves $2$
Conductor $257600$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 257600.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
257600.u1 257600u1 \([0, 1, 0, -56208, 5105338]\) \(157114339136/181447\) \(22680875000000\) \([2]\) \(860160\) \(1.4754\) \(\Gamma_0(N)\)-optimal
257600.u2 257600u2 \([0, 1, 0, -41833, 7793463]\) \(-1012048064/2705927\) \(-21647416000000000\) \([2]\) \(1720320\) \(1.8219\)  

Rank

sage: E.rank()
 

The elliptic curves in class 257600.u have rank \(0\).

Complex multiplication

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

Modular form 257600.2.a.u

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} - q^{7} + q^{9} + 2 q^{11} + 2 q^{13} - 2 q^{17} + 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.