Properties

Label 26640.bb
Number of curves $2$
Conductor $26640$
CM no
Rank $1$
Graph

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

Elliptic curves in class 26640.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26640.bb1 26640y2 \([0, 0, 0, -58982067, -174352466574]\) \(281470209323873024547/35046400\) \(2825495720755200\) \([2]\) \(2027520\) \(2.8262\)  
26640.bb2 26640y1 \([0, 0, 0, -3686067, -2724741774]\) \(-68700855708416547/24248320000\) \(-1954937579765760000\) \([2]\) \(1013760\) \(2.4797\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 26640.bb have rank \(1\).

Complex multiplication

The elliptic curves in class 26640.bb do not have complex multiplication.

Modular form 26640.2.a.bb

sage: E.q_eigenform(10)
 
\(q + q^{5} - 4 q^{7} + 6 q^{13} - 6 q^{17} - 6 q^{19} + O(q^{20})\) 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.