Properties

Label 53900f
Number of curves $2$
Conductor $53900$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 53900f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53900.v2 53900f1 \([0, 0, 0, 9800, -385875]\) \(3538944/4235\) \(-124560878750000\) \([2]\) \(110592\) \(1.3909\) \(\Gamma_0(N)\)-optimal
53900.v1 53900f2 \([0, 0, 0, -57575, -3687250]\) \(44851536/13475\) \(6341281100000000\) \([2]\) \(221184\) \(1.7374\)  

Rank

sage: E.rank()
 

The elliptic curves in class 53900f have rank \(1\).

Complex multiplication

The elliptic curves in class 53900f do not have complex multiplication.

Modular form 53900.2.a.f

sage: E.q_eigenform(10)
 
\(q - 3 q^{9} - q^{11} + 2 q^{13} - 6 q^{17} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.