Properties

Label 53816.a
Number of curves $2$
Conductor $53816$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 53816.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53816.a1 53816a2 \([0, 1, 0, -38760, 2888944]\) \(3543122/49\) \(89062769395712\) \([2]\) \(241920\) \(1.4823\)  
53816.a2 53816a1 \([0, 1, 0, -320, 121264]\) \(-4/7\) \(-6361626385408\) \([2]\) \(120960\) \(1.1358\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 53816.a have rank \(1\).

Complex multiplication

The elliptic curves in class 53816.a do not have complex multiplication.

Modular form 53816.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} - 4 q^{5} + q^{7} + q^{9} + 8 q^{15} + 2 q^{17} - 2 q^{19} + O(q^{20})\) 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 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.