Properties

Label 11025.bn
Number of curves $2$
Conductor $11025$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bn1")
 
E.isogeny_class()
 

Elliptic curves in class 11025.bn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11025.bn1 11025bc2 \([0, 0, 1, -91875, -10986719]\) \(-102400/3\) \(-2512679326171875\) \([]\) \(79200\) \(1.7339\)  
11025.bn2 11025bc1 \([0, 0, 1, 735, 33871]\) \(20480/243\) \(-521029185075\) \([]\) \(15840\) \(0.92916\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 11025.bn have rank \(1\).

Complex multiplication

The elliptic curves in class 11025.bn do not have complex multiplication.

Modular form 11025.2.a.bn

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} + 2 q^{4} - 2 q^{11} + q^{13} - 4 q^{16} - 2 q^{17} + 5 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.