Properties

Label 26520.t
Number of curves $2$
Conductor $26520$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 26520.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26520.t1 26520g1 \([0, 1, 0, -2691, -54630]\) \(134742996281344/21133125\) \(338130000\) \([2]\) \(16384\) \(0.64749\) \(\Gamma_0(N)\)-optimal
26520.t2 26520g2 \([0, 1, 0, -2436, -65136]\) \(-6247321674064/3366796875\) \(-861900000000\) \([2]\) \(32768\) \(0.99407\)  

Rank

sage: E.rank()
 

The elliptic curves in class 26520.t have rank \(0\).

Complex multiplication

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

Modular form 26520.2.a.t

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} - 2 q^{7} + q^{9} + q^{13} - q^{15} + q^{17} + 4 q^{19} + O(q^{20})\) 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.