Properties

Label 53816c
Number of curves $4$
Conductor $53816$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 53816c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
53816.d4 53816c1 [0, 0, 0, 961, -59582] [2] 57600 \(\Gamma_0(N)\)-optimal
53816.d3 53816c2 [0, 0, 0, -18259, -893730] [2, 2] 115200  
53816.d2 53816c3 [0, 0, 0, -56699, 4111158] [2] 230400  
53816.d1 53816c4 [0, 0, 0, -287339, -59284090] [2] 230400  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 53816.2.a.c

sage: E.q_eigenform(10)
 
\( q + 2q^{5} - q^{7} - 3q^{9} + 4q^{11} - 2q^{13} + 6q^{17} + 8q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.