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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 203280.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 203280.w1 | 203280eg4 | \([0, -1, 0, -3975616, -3049763264]\) | \(957681397954009/31185\) | \(226288147599360\) | \([2]\) | \(2949120\) | \(2.2557\) | |
| 203280.w2 | 203280eg3 | \([0, -1, 0, -394016, 14460096]\) | \(932288503609/527295615\) | \(3826222477332541440\) | \([2]\) | \(2949120\) | \(2.2557\) | |
| 203280.w3 | 203280eg2 | \([0, -1, 0, -248816, -47453184]\) | \(234770924809/1334025\) | \(9680104091750400\) | \([2, 2]\) | \(1474560\) | \(1.9091\) | |
| 203280.w4 | 203280eg1 | \([0, -1, 0, -6816, -1569984]\) | \(-4826809/144375\) | \(-1047630312960000\) | \([2]\) | \(737280\) | \(1.5625\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 203280.w have rank \(1\).
Complex multiplication
The elliptic curves in class 203280.w do not have complex multiplication.Modular form 203280.2.a.w
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
