Properties

Label 9920.d
Number of curves $2$
Conductor $9920$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 9920.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9920.d1 9920j2 \([0, 1, 0, -68225, -6881825]\) \(133974081659809/192200\) \(50384076800\) \([2]\) \(18432\) \(1.3247\)  
9920.d2 9920j1 \([0, 1, 0, -4225, -110625]\) \(-31824875809/1240000\) \(-325058560000\) \([2]\) \(9216\) \(0.97809\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 9920.d have rank \(0\).

Complex multiplication

The elliptic curves in class 9920.d do not have complex multiplication.

Modular form 9920.2.a.d

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