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Properties

Label 990.d
Number of curves $2$
Conductor $990$
CM no
Rank $0$
Graph

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

Elliptic curves in class 990.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
990.d1 990d2 \([1, -1, 0, -53460, 4771030]\) \(-23178622194826561/1610510\) \(-1174061790\) \([]\) \(3000\) \(1.1944\)  
990.d2 990d1 \([1, -1, 0, 90, 1300]\) \(109902239/1100000\) \(-801900000\) \([]\) \(600\) \(0.38966\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 990.d have rank \(0\).

Complex multiplication

The elliptic curves in class 990.d do not have complex multiplication.

Modular form 990.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} + 3 q^{7} - q^{8} + q^{10} - q^{11} - 6 q^{13} - 3 q^{14} + q^{16} + 7 q^{17} + 5 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.