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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 180708.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 180708.a1 | 180708c2 | \([0, -1, 0, -18011020, 28271522056]\) | \(983758169579344/43835197923\) | \(28792095988424460417792\) | \([2]\) | \(29417472\) | \(3.0722\) | |
| 180708.a2 | 180708c1 | \([0, -1, 0, -3041005, -1458927734]\) | \(75760866033664/21413352213\) | \(879052852449803089872\) | \([2]\) | \(14708736\) | \(2.7256\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 180708.a have rank \(0\).
Complex multiplication
The elliptic curves in class 180708.a do not have complex multiplication.Modular form 180708.2.a.a
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.
