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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 405600c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
405600.c2 | 405600c1 | \([0, -1, 0, -837958, 295246912]\) | \(107850176/117\) | \(70592081625000000\) | \([2]\) | \(6021120\) | \(2.1486\) | \(\Gamma_0(N)\)-optimal |
405600.c1 | 405600c2 | \([0, -1, 0, -1049208, 135119412]\) | \(26463592/13689\) | \(66074188401000000000\) | \([2]\) | \(12042240\) | \(2.4951\) |
Rank
sage: E.rank()
The elliptic curves in class 405600c have rank \(0\).
Complex multiplication
The elliptic curves in class 405600c do not have complex multiplication.Modular form 405600.2.a.c
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.