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SageMath
E = EllipticCurve("dd1")
E.isogeny_class()
Elliptic curves in class 54208dd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54208.k2 | 54208dd1 | \([0, 1, 0, -5969, -299345]\) | \(-810448/847\) | \(-24584391344128\) | \([2]\) | \(122880\) | \(1.2647\) | \(\Gamma_0(N)\)-optimal |
54208.k1 | 54208dd2 | \([0, 1, 0, -112449, -14546369]\) | \(1354435492/539\) | \(62578450694144\) | \([2]\) | \(245760\) | \(1.6112\) |
Rank
sage: E.rank()
The elliptic curves in class 54208dd have rank \(0\).
Complex multiplication
The elliptic curves in class 54208dd do not have complex multiplication.Modular form 54208.2.a.dd
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 Cremona 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 Cremona labels.