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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 18496.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18496.c1 | 18496f2 | \([0, 1, 0, -1473, -22241]\) | \(1098500\) | \(321978368\) | \([2]\) | \(8192\) | \(0.55637\) | |
18496.c2 | 18496f1 | \([0, 1, 0, -113, -209]\) | \(2000\) | \(80494592\) | \([2]\) | \(4096\) | \(0.20979\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 18496.c have rank \(1\).
Complex multiplication
The elliptic curves in class 18496.c do not have complex multiplication.Modular form 18496.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.