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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 53900bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 53900.x2 | 53900bc1 | \([0, 0, 0, -24500, -1071875]\) | \(442368/121\) | \(444860281250000\) | \([2]\) | \(172800\) | \(1.5184\) | \(\Gamma_0(N)\)-optimal |
| 53900.x1 | 53900bc2 | \([0, 0, 0, -361375, -83606250]\) | \(88723728/11\) | \(647069500000000\) | \([2]\) | \(345600\) | \(1.8650\) |
Rank
sage: E.rank()
The elliptic curves in class 53900bc have rank \(0\).
Complex multiplication
The elliptic curves in class 53900bc do not have complex multiplication.Modular form 53900.2.a.bc
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.
