Properties

Label 26520.u
Number of curves $2$
Conductor $26520$
CM no
Rank $1$
Graph

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

Elliptic curves in class 26520.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26520.u1 26520y1 \([0, 1, 0, -281016, 57158784]\) \(2396726313900986596/4154072495625\) \(4253770235520000\) \([2]\) \(184320\) \(1.8928\) \(\Gamma_0(N)\)-optimal
26520.u2 26520y2 \([0, 1, 0, -193136, 93646560]\) \(-389032340685029858/1627263833203125\) \(-3332636330400000000\) \([2]\) \(368640\) \(2.2393\)  

Rank

sage: E.rank()
 

The elliptic curves in class 26520.u have rank \(1\).

Complex multiplication

The elliptic curves in class 26520.u do not have complex multiplication.

Modular form 26520.2.a.u

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + q^{9} + 2 q^{11} - q^{13} - q^{15} - q^{17} - 8 q^{19} + O(q^{20})\) 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.