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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 1856.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1856.k1 | 1856a2 | \([0, 1, 0, -29121, -1935457]\) | \(-10418796526321/82044596\) | \(-21507498573824\) | \([]\) | \(3840\) | \(1.3869\) | |
| 1856.k2 | 1856a1 | \([0, 1, 0, 319, 3743]\) | \(13651919/29696\) | \(-7784628224\) | \([]\) | \(768\) | \(0.58217\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1856.k have rank \(0\).
Complex multiplication
The elliptic curves in class 1856.k do not have complex multiplication.Modular form 1856.2.a.k
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
