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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 16731.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16731.m1 | 16731d2 | \([1, -1, 0, -2820, 58033]\) | \(19034163/121\) | \(15769185003\) | \([2]\) | \(18432\) | \(0.79378\) | |
16731.m2 | 16731d1 | \([1, -1, 0, -285, -272]\) | \(19683/11\) | \(1433562273\) | \([2]\) | \(9216\) | \(0.44721\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 16731.m have rank \(0\).
Complex multiplication
The elliptic curves in class 16731.m do not have complex multiplication.Modular form 16731.2.a.m
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.