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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 63525.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
63525.c1 | 63525v2 | \([0, -1, 1, -81040758, 5308802648918]\) | \(-2126464142970105856/438611057788643355\) | \(-12141035064798543916049296875\) | \([]\) | \(86400000\) | \(4.0682\) | |
63525.c2 | 63525v1 | \([0, -1, 1, -27044508, -63385903582]\) | \(-79028701534867456/16987307596875\) | \(-470219556775429248046875\) | \([]\) | \(17280000\) | \(3.2634\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 63525.c have rank \(1\).
Complex multiplication
The elliptic curves in class 63525.c do not have complex multiplication.Modular form 63525.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.