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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 48576bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 48576.cu2 | 48576bd1 | \([0, 1, 0, -1473, -317025]\) | \(-1349232625/164333367\) | \(-43079006158848\) | \([2]\) | \(81920\) | \(1.2956\) | \(\Gamma_0(N)\)-optimal |
| 48576.cu1 | 48576bd2 | \([0, 1, 0, -79233, -8544033]\) | \(209849322390625/1882056627\) | \(493369852428288\) | \([2]\) | \(163840\) | \(1.6422\) |
Rank
sage: E.rank()
The elliptic curves in class 48576bd have rank \(1\).
Complex multiplication
The elliptic curves in class 48576bd do not have complex multiplication.Modular form 48576.2.a.bd
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.
