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SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 29400co
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
29400.ba1 | 29400co1 | \([0, -1, 0, -1283, 13812]\) | \(2725888/675\) | \(57881250000\) | \([2]\) | \(18432\) | \(0.77547\) | \(\Gamma_0(N)\)-optimal |
29400.ba2 | 29400co2 | \([0, -1, 0, 3092, 83812]\) | \(2382032/3645\) | \(-5000940000000\) | \([2]\) | \(36864\) | \(1.1220\) |
Rank
sage: E.rank()
The elliptic curves in class 29400co have rank \(1\).
Complex multiplication
The elliptic curves in class 29400co do not have complex multiplication.Modular form 29400.2.a.co
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.