Properties

Label 54208.t
Number of curves $2$
Conductor $54208$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 54208.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54208.t1 54208bn2 \([0, 1, 0, -398977, -89674785]\) \(15124197817/1294139\) \(601003440466558976\) \([2]\) \(737280\) \(2.1526\)  
54208.t2 54208bn1 \([0, 1, 0, 26943, -6450017]\) \(4657463/41503\) \(-19274162813796352\) \([2]\) \(368640\) \(1.8061\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 54208.t have rank \(1\).

Complex multiplication

The elliptic curves in class 54208.t do not have complex multiplication.

Modular form 54208.2.a.t

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} + 2 q^{5} + q^{7} + q^{9} + 4 q^{13} - 4 q^{15} - 4 q^{17} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.