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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 16245.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16245.k1 | 16245k2 | \([1, -1, 0, -303849, -62723970]\) | \(90458382169/2671875\) | \(91635819993421875\) | \([2]\) | \(138240\) | \(2.0319\) | |
| 16245.k2 | 16245k1 | \([1, -1, 0, 4806, -3277017]\) | \(357911/135375\) | \(-4642881546333375\) | \([2]\) | \(69120\) | \(1.6853\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 16245.k have rank \(0\).
Complex multiplication
The elliptic curves in class 16245.k do not have complex multiplication.Modular form 16245.2.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.
