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SageMath
E = EllipticCurve("dt1")
E.isogeny_class()
Elliptic curves in class 324870.dt
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
324870.dt1 | 324870dt1 | \([1, 1, 1, -32215051, -70391328967]\) | \(31427652507069423952801/654426190080\) | \(76992586836721920\) | \([2]\) | \(17510400\) | \(2.7696\) | \(\Gamma_0(N)\)-optimal |
324870.dt2 | 324870dt2 | \([1, 1, 1, -32179771, -70553151271]\) | \(-31324512477868037557921/143427974919699600\) | \(-16874157821327738240400\) | \([2]\) | \(35020800\) | \(3.1161\) |
Rank
sage: E.rank()
The elliptic curves in class 324870.dt have rank \(1\).
Complex multiplication
The elliptic curves in class 324870.dt do not have complex multiplication.Modular form 324870.2.a.dt
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.