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Properties

Label 106.d
Number of curves $2$
Conductor $106$
CM no
Rank $0$
Graph

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

Elliptic curves in class 106.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
106.d1 106c2 \([1, 0, 0, -24603, -1487407]\) \(-1646982616152408625/38112512\) \(-38112512\) \([]\) \(144\) \(0.97740\)  
106.d2 106c1 \([1, 0, 0, -283, -2351]\) \(-2507141976625/889192448\) \(-889192448\) \([3]\) \(48\) \(0.42809\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 106.d have rank \(0\).

Complex multiplication

The elliptic curves in class 106.d do not have complex multiplication.

Modular form 106.2.a.d

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} - 4 q^{7} + q^{8} - 2 q^{9} + q^{12} + 5 q^{13} - 4 q^{14} + q^{16} - 3 q^{17} - 2 q^{18} - q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.