Properties

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

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Show commands: SageMath
E = EllipticCurve("bd1")
 
E.isogeny_class()
 

Elliptic curves in class 53900bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53900.n2 53900bd1 \([0, 0, 0, -980, -8575]\) \(442368/121\) \(28471058000\) \([2]\) \(34560\) \(0.71372\) \(\Gamma_0(N)\)-optimal
53900.n1 53900bd2 \([0, 0, 0, -14455, -668850]\) \(88723728/11\) \(41412448000\) \([2]\) \(69120\) \(1.0603\)  

Rank

sage: E.rank()
 

The elliptic curves in class 53900bd have rank \(2\).

Complex multiplication

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

Modular form 53900.2.a.bd

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