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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 260.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
260.a1 | 260a1 | \([0, -1, 0, -281, 1910]\) | \(153910165504/845\) | \(13520\) | \([2]\) | \(48\) | \(-0.014007\) | \(\Gamma_0(N)\)-optimal |
260.a2 | 260a2 | \([0, -1, 0, -276, 1976]\) | \(-9115564624/714025\) | \(-182790400\) | \([2]\) | \(96\) | \(0.33257\) |
Rank
sage: E.rank()
The elliptic curves in class 260.a have rank \(0\).
Complex multiplication
The elliptic curves in class 260.a do not have complex multiplication.Modular form 260.2.a.a
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.