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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 69360bz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
69360.o2 | 69360bz1 | \([0, -1, 0, -13101, -363744]\) | \(131072/45\) | \(85383271077840\) | \([2]\) | \(182784\) | \(1.3751\) | \(\Gamma_0(N)\)-optimal |
69360.o1 | 69360bz2 | \([0, -1, 0, -86796, 9599820]\) | \(2382032/75\) | \(2276887228742400\) | \([2]\) | \(365568\) | \(1.7217\) |
Rank
sage: E.rank()
The elliptic curves in class 69360bz have rank \(0\).
Complex multiplication
The elliptic curves in class 69360bz do not have complex multiplication.Modular form 69360.2.a.bz
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.