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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 277725bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 277725.bf1 | 277725bf1 | \([0, -1, 1, -42787283, 107756610218]\) | \(-7079867613184/1250235\) | \(-1529798979418609921875\) | \([]\) | \(17169408\) | \(3.0698\) | \(\Gamma_0(N)\)-optimal |
| 277725.bf2 | 277725bf2 | \([0, -1, 1, 11964217, 358231034843]\) | \(154786758656/45397807875\) | \(-55549172879512357623046875\) | \([]\) | \(51508224\) | \(3.6191\) |
Rank
sage: E.rank()
The elliptic curves in class 277725bf have rank \(0\).
Complex multiplication
The elliptic curves in class 277725bf do not have complex multiplication.Modular form 277725.2.a.bf
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
