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Properties

Label 208d
Number of curves $2$
Conductor $208$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 208d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
208.d2 208d1 \([0, 0, 0, -43, -166]\) \(-2146689/1664\) \(-6815744\) \([]\) \(48\) \(0.0099866\) \(\Gamma_0(N)\)-optimal
208.d1 208d2 \([0, 0, 0, -3403, 83834]\) \(-1064019559329/125497034\) \(-514035851264\) \([]\) \(336\) \(0.98294\)  

Rank

sage: E.rank()
 

The elliptic curves in class 208d have rank \(0\).

Complex multiplication

The elliptic curves in class 208d do not have complex multiplication.

Modular form 208.2.a.d

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

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.