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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 25872.bz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
25872.bz1 | 25872l1 | \([0, 1, 0, -408, 804]\) | \(62500/33\) | \(3975595008\) | \([2]\) | \(11520\) | \(0.53351\) | \(\Gamma_0(N)\)-optimal |
25872.bz2 | 25872l2 | \([0, 1, 0, 1552, 7860]\) | \(1714750/1089\) | \(-262389270528\) | \([2]\) | \(23040\) | \(0.88008\) |
Rank
sage: E.rank()
The elliptic curves in class 25872.bz have rank \(1\).
Complex multiplication
The elliptic curves in class 25872.bz do not have complex multiplication.Modular form 25872.2.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 LMFDB 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 LMFDB labels.