Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("53312.n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 53312ci

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
53312.n2 53312ci1 [0, 1, 0, -54553, 4886055] [2] 172032 \(\Gamma_0(N)\)-optimal
53312.n1 53312ci2 [0, 1, 0, -56513, 4514047] [2] 344064  

Rank

sage: E.rank()
 

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

Modular form 53312.2.a.n

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

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.