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SageMath
E = EllipticCurve("dz1")
E.isogeny_class()
Elliptic curves in class 254800dz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
254800.dz2 | 254800dz1 | \([0, 0, 0, -1715, -17150]\) | \(37044/13\) | \(195767936000\) | \([2]\) | \(184320\) | \(0.86803\) | \(\Gamma_0(N)\)-optimal |
254800.dz1 | 254800dz2 | \([0, 0, 0, -11515, 463050]\) | \(5606442/169\) | \(5089966336000\) | \([2]\) | \(368640\) | \(1.2146\) |
Rank
sage: E.rank()
The elliptic curves in class 254800dz have rank \(1\).
Complex multiplication
The elliptic curves in class 254800dz do not have complex multiplication.Modular form 254800.2.a.dz
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.