Properties

Label 53312.s
Number of curves $2$
Conductor $53312$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("53312.s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 53312.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
53312.s1 53312cj2 [0, 1, 0, -3201, -48833] [2] 110592  
53312.s2 53312cj1 [0, 1, 0, -1241, 15847] [2] 55296 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 53312.s have rank \(0\).

Modular form 53312.2.a.s

sage: E.q_eigenform(10)
 
\( q - 2q^{3} + 4q^{5} + q^{9} + 2q^{11} + 2q^{13} - 8q^{15} + q^{17} - 8q^{19} + O(q^{20}) \)

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 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.