Properties

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

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Show commands: SageMath
E = EllipticCurve("bg1")
 
E.isogeny_class()
 

Elliptic curves in class 11025bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11025.bg2 11025bg1 \([1, -1, 0, -3537, 89046]\) \(-9317\) \(-525317491125\) \([]\) \(10080\) \(0.98729\) \(\Gamma_0(N)\)-optimal
11025.bg1 11025bg2 \([1, -1, 0, -91764612, -338322994479]\) \(-162677523113838677\) \(-525317491125\) \([]\) \(372960\) \(2.7927\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 11025.2.a.bg

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} - 3 q^{8} - 2 q^{13} - q^{16} + 2 q^{17} + 6 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 37 \\ 37 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.