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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 2574.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2574.d1 | 2574f2 | \([1, -1, 0, -66348, 6586704]\) | \(44308125149913793/61165323648\) | \(44589520939392\) | \([2]\) | \(16128\) | \(1.5234\) | |
| 2574.d2 | 2574f1 | \([1, -1, 0, -2988, 162000]\) | \(-4047806261953/13066420224\) | \(-9525420343296\) | \([2]\) | \(8064\) | \(1.1768\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2574.d have rank \(0\).
Complex multiplication
The elliptic curves in class 2574.d do not have complex multiplication.Modular form 2574.2.a.d
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.
