Properties

Label 108900ct
Number of curves $4$
Conductor $108900$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ct1")
 
E.isogeny_class()
 

Elliptic curves in class 108900ct

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
108900.f4 108900ct1 \([0, 0, 0, -1234200, 516927125]\) \(643956736/15125\) \(4883363257781250000\) \([2]\) \(2488320\) \(2.3715\) \(\Gamma_0(N)\)-optimal
108900.f3 108900ct2 \([0, 0, 0, -2731575, -981945250]\) \(436334416/171875\) \(887884228687500000000\) \([2]\) \(4976640\) \(2.7181\)  
108900.f2 108900ct3 \([0, 0, 0, -12124200, -16044040375]\) \(610462990336/8857805\) \(2859892858287011250000\) \([2]\) \(7464960\) \(2.9208\)  
108900.f1 108900ct4 \([0, 0, 0, -193306575, -1034470170250]\) \(154639330142416/33275\) \(171894386673900000000\) \([2]\) \(14929920\) \(3.2674\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 108900.2.a.ct

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.