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SageMath
E = EllipticCurve("cd1")
E.isogeny_class()
Elliptic curves in class 95370.cd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
95370.cd1 | 95370cf2 | \([1, 1, 1, -3398646, 2408803443]\) | \(179865548102096641/119964240000\) | \(2895645120532560000\) | \([2]\) | \(3096576\) | \(2.4812\) | |
95370.cd2 | 95370cf1 | \([1, 1, 1, -254326, 21635699]\) | \(75370704203521/35157196800\) | \(848609263606579200\) | \([2]\) | \(1548288\) | \(2.1346\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 95370.cd have rank \(1\).
Complex multiplication
The elliptic curves in class 95370.cd do not have complex multiplication.Modular form 95370.2.a.cd
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.