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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 98736.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
98736.t1 | 98736bn1 | \([0, -1, 0, -6024, 24048]\) | \(4435194707/2528172\) | \(13783027433472\) | \([2]\) | \(258048\) | \(1.2110\) | \(\Gamma_0(N)\)-optimal |
98736.t2 | 98736bn2 | \([0, -1, 0, 23896, 167664]\) | \(276785390413/162620946\) | \(-886572970500096\) | \([2]\) | \(516096\) | \(1.5576\) |
Rank
sage: E.rank()
The elliptic curves in class 98736.t have rank \(0\).
Complex multiplication
The elliptic curves in class 98736.t do not have complex multiplication.Modular form 98736.2.a.t
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.