Properties

Label 10920.e
Number of curves $2$
Conductor $10920$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 10920.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10920.e1 10920l1 \([0, -1, 0, -19656, -492804]\) \(820221748268836/369468094905\) \(378335329182720\) \([2]\) \(37632\) \(1.4925\) \(\Gamma_0(N)\)-optimal
10920.e2 10920l2 \([0, -1, 0, 68224, -3761940]\) \(17147425715207422/12872524043925\) \(-26362929241958400\) \([2]\) \(75264\) \(1.8391\)  

Rank

sage: E.rank()
 

The elliptic curves in class 10920.e have rank \(0\).

Complex multiplication

The elliptic curves in class 10920.e do not have complex multiplication.

Modular form 10920.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{7} + q^{9} + 2q^{11} + q^{13} + q^{15} - 2q^{17} - 6q^{19} + O(q^{20})\)  Toggle raw display

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.