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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 257600.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 257600.k1 | 257600k2 | \([0, 1, 0, -112033, -14363937]\) | \(75933869762/648025\) | \(1327155200000000\) | \([2]\) | \(1769472\) | \(1.7267\) | |
| 257600.k2 | 257600k1 | \([0, 1, 0, -12033, 136063]\) | \(188183524/100625\) | \(103040000000000\) | \([2]\) | \(884736\) | \(1.3801\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 257600.k have rank \(1\).
Complex multiplication
The elliptic curves in class 257600.k do not have complex multiplication.Modular form 257600.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
