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SageMath
E = EllipticCurve("nf1")
E.isogeny_class()
Elliptic curves in class 310464.nf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
310464.nf1 | 310464nf2 | \([0, 0, 0, -29484, 1883952]\) | \(3203226/121\) | \(107073181974528\) | \([2]\) | \(884736\) | \(1.4605\) | |
310464.nf2 | 310464nf1 | \([0, 0, 0, 756, 105840]\) | \(108/11\) | \(-4866962817024\) | \([2]\) | \(442368\) | \(1.1139\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 310464.nf have rank \(0\).
Complex multiplication
The elliptic curves in class 310464.nf do not have complex multiplication.Modular form 310464.2.a.nf
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.