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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 6380c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6380.b1 | 6380c1 | \([0, 1, 0, -876001, 315284940]\) | \(4646415367355940880384/38478378125\) | \(615654050000\) | \([2]\) | \(47040\) | \(1.8500\) | \(\Gamma_0(N)\)-optimal |
| 6380.b2 | 6380c2 | \([0, 1, 0, -875396, 315742804]\) | \(-289799689905740628304/835751962890625\) | \(-213952502500000000\) | \([2]\) | \(94080\) | \(2.1965\) |
Rank
sage: E.rank()
The elliptic curves in class 6380c have rank \(0\).
Complex multiplication
The elliptic curves in class 6380c do not have complex multiplication.Modular form 6380.2.a.c
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.
