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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 439569.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
439569.o1 | 439569o2 | \([1, -1, 1, -1793291, -923875234]\) | \(36892780289/13\) | \(224738645271309\) | \([2]\) | \(4128768\) | \(2.1086\) | |
439569.o2 | 439569o1 | \([1, -1, 1, -112586, -14277688]\) | \(9129329/169\) | \(2921602388527017\) | \([2]\) | \(2064384\) | \(1.7620\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 439569.o have rank \(0\).
Complex multiplication
The elliptic curves in class 439569.o do not have complex multiplication.Modular form 439569.2.a.o
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.