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SageMath
E = EllipticCurve("ct1")
E.isogeny_class()
Elliptic curves in class 286110ct
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
286110.ct2 | 286110ct1 | \([1, -1, 0, -43404, -7562692]\) | \(-19034163/41140\) | \(-19545604563594780\) | \([2]\) | \(2654208\) | \(1.8148\) | \(\Gamma_0(N)\)-optimal |
286110.ct1 | 286110ct2 | \([1, -1, 0, -901734, -329093110]\) | \(170676802323/158950\) | \(75517108541161650\) | \([2]\) | \(5308416\) | \(2.1614\) |
Rank
sage: E.rank()
The elliptic curves in class 286110ct have rank \(1\).
Complex multiplication
The elliptic curves in class 286110ct do not have complex multiplication.Modular form 286110.2.a.ct
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.