Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("53312.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 53312.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
53312.g1 53312bd2 [0, 1, 0, -2195265, -1250122721] [2] 2064384  
53312.g2 53312bd1 [0, 1, 0, -188225, -3750881] [2] 1032192 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 53312.2.a.g

sage: E.q_eigenform(10)
 
\( q - 2q^{3} - 4q^{5} + q^{9} + 6q^{11} - 2q^{13} + 8q^{15} + q^{17} + O(q^{20}) \)

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.