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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 26520.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
26520.k1 | 26520r1 | \([0, -1, 0, -3089195, -2088807468]\) | \(203769809659907949070336/2016474841511325\) | \(32263597464181200\) | \([2]\) | \(506880\) | \(2.3277\) | \(\Gamma_0(N)\)-optimal |
26520.k2 | 26520r2 | \([0, -1, 0, -3015500, -2193277500]\) | \(-11845731628994222232016/1269935194601506875\) | \(-325103409817985760000\) | \([2]\) | \(1013760\) | \(2.6743\) |
Rank
sage: E.rank()
The elliptic curves in class 26520.k have rank \(0\).
Complex multiplication
The elliptic curves in class 26520.k do not have complex multiplication.Modular form 26520.2.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.