Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("53312.r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 53312.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
53312.r1 53312ck2 [0, 1, 0, -403041, -18841313] [2] 1474560  
53312.r2 53312ck1 [0, 1, 0, 98719, -2283233] [2] 737280 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 53312.2.a.r

sage: E.q_eigenform(10)
 
\( q - 2q^{3} + 4q^{5} + q^{9} - 4q^{11} - 4q^{13} - 8q^{15} + q^{17} + 6q^{19} + O(q^{20}) \)

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.