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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 67280l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
67280.j1 | 67280l1 | \([0, 0, 0, -36163, -2487678]\) | \(2146689/145\) | \(353277466808320\) | \([2]\) | \(215040\) | \(1.5403\) | \(\Gamma_0(N)\)-optimal |
67280.j2 | 67280l2 | \([0, 0, 0, 31117, -10682382]\) | \(1367631/21025\) | \(-51225232687206400\) | \([2]\) | \(430080\) | \(1.8869\) |
Rank
sage: E.rank()
The elliptic curves in class 67280l have rank \(0\).
Complex multiplication
The elliptic curves in class 67280l do not have complex multiplication.Modular form 67280.2.a.l
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 Cremona 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 Cremona labels.