Properties

Label 53312bw
Number of curves $2$
Conductor $53312$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("53312.p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 53312bw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
53312.p2 53312bw1 [0, 1, 0, -212, 2470] [2] 23040 \(\Gamma_0(N)\)-optimal
53312.p1 53312bw2 [0, 1, 0, -4377, 109927] [2] 46080  

Rank

sage: E.rank()
 

The elliptic curves in class 53312bw have rank \(1\).

Modular form 53312.2.a.p

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.