Properties

Label 108900bt
Number of curves $2$
Conductor $108900$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bt1")
 
E.isogeny_class()
 

Elliptic curves in class 108900bt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
108900.bi2 108900bt1 \([0, 0, 0, 825, -63250]\) \(176/5\) \(-1764180000000\) \([]\) \(103680\) \(1.0300\) \(\Gamma_0(N)\)-optimal
108900.bi1 108900bt2 \([0, 0, 0, -98175, -11844250]\) \(-296587984/125\) \(-44104500000000\) \([]\) \(311040\) \(1.5793\)  

Rank

sage: E.rank()
 

The elliptic curves in class 108900bt have rank \(0\).

Complex multiplication

The elliptic curves in class 108900bt do not have complex multiplication.

Modular form 108900.2.a.bt

sage: E.q_eigenform(10)
 
\(q - q^{7} + 2 q^{13} - 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.