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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 208.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 208.d1 | 208d2 | \([0, 0, 0, -3403, 83834]\) | \(-1064019559329/125497034\) | \(-514035851264\) | \([]\) | \(336\) | \(0.98294\) | |
| 208.d2 | 208d1 | \([0, 0, 0, -43, -166]\) | \(-2146689/1664\) | \(-6815744\) | \([]\) | \(48\) | \(0.0099866\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 208.d have rank \(0\).
Complex multiplication
The elliptic curves in class 208.d do not have complex multiplication.Modular form 208.2.a.d
sage: E.q_eigenform(10)
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
