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SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 122304.ca
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 122304.ca1 | 122304fx2 | \([0, -1, 0, -19273, 458473]\) | \(1643032000/767637\) | \(369916827291648\) | \([2]\) | \(460800\) | \(1.4898\) | |
| 122304.ca2 | 122304fx1 | \([0, -1, 0, -16088, 790350]\) | \(61162984000/41067\) | \(309215454912\) | \([2]\) | \(230400\) | \(1.1432\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 122304.ca have rank \(0\).
Complex multiplication
The elliptic curves in class 122304.ca do not have complex multiplication.Modular form 122304.2.a.ca
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.
