Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("bb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 26520.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26520.bb1 26520be2 \([0, 1, 0, -8285158460, -290175586566192]\) \(245689277968779868090419995701456/93342399137270122585475925\) \(23895654179141151381881836800\) \([2]\) \(30965760\) \(4.4115\)  
26520.bb2 26520be1 \([0, 1, 0, -441593835, -5915392278642]\) \(-595213448747095198927846967296/600281130562949295663181875\) \(-9604498089007188730610910000\) \([2]\) \(15482880\) \(4.0650\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 26520.2.a.bb

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