Properties

Label 26928bp
Number of curves $4$
Conductor $26928$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("bp1")
 
E.isogeny_class()
 

Elliptic curves in class 26928bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26928.l3 26928bp1 \([0, 0, 0, -55731, 5063794]\) \(6411014266033/296208\) \(884472348672\) \([2]\) \(73728\) \(1.3676\) \(\Gamma_0(N)\)-optimal
26928.l2 26928bp2 \([0, 0, 0, -58611, 4511410]\) \(7457162887153/1370924676\) \(4093559147741184\) \([2, 2]\) \(147456\) \(1.7141\)  
26928.l4 26928bp3 \([0, 0, 0, 115629, 26221714]\) \(57258048889007/132611470002\) \(-395975727642451968\) \([2]\) \(294912\) \(2.0607\)  
26928.l1 26928bp4 \([0, 0, 0, -278931, -52551470]\) \(803760366578833/65593817586\) \(195862089810714624\) \([2]\) \(294912\) \(2.0607\)  

Rank

sage: E.rank()
 

The elliptic curves in class 26928bp have rank \(2\).

Complex multiplication

The elliptic curves in class 26928bp do not have complex multiplication.

Modular form 26928.2.a.bp

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} - 4 q^{7} + q^{11} - 2 q^{13} - q^{17} - 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.