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SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 162240ca
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162240.cf2 | 162240ca1 | \([0, -1, 0, 295, -3303]\) | \(314432/675\) | \(-6074265600\) | \([2]\) | \(129024\) | \(0.56153\) | \(\Gamma_0(N)\)-optimal |
| 162240.cf1 | 162240ca2 | \([0, -1, 0, -2305, -33983]\) | \(18821096/3645\) | \(262408273920\) | \([2]\) | \(258048\) | \(0.90810\) |
Rank
sage: E.rank()
The elliptic curves in class 162240ca have rank \(0\).
Complex multiplication
The elliptic curves in class 162240ca do not have complex multiplication.Modular form 162240.2.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 Cremona 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 Cremona labels.
