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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 203280.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 203280.d1 | 203280dw2 | \([0, -1, 0, -292376, 76216560]\) | \(-3148102969/1029000\) | \(-903476381896704000\) | \([]\) | \(3421440\) | \(2.1579\) | |
| 203280.d2 | 203280dw1 | \([0, -1, 0, 27064, -960144]\) | \(2496791/1890\) | \(-1659446415728640\) | \([]\) | \(1140480\) | \(1.6086\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 203280.d have rank \(1\).
Complex multiplication
The elliptic curves in class 203280.d do not have complex multiplication.Modular form 203280.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
