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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 106.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
106.c1 | 106a2 | \([1, 0, 0, -9, -29]\) | \(-81182737/297754\) | \(-297754\) | \([]\) | \(18\) | \(-0.26391\) | |
106.c2 | 106a1 | \([1, 0, 0, 1, 1]\) | \(103823/424\) | \(-424\) | \([3]\) | \(6\) | \(-0.81321\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 106.c have rank \(0\).
Complex multiplication
The elliptic curves in class 106.c do not have complex multiplication.Modular form 106.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.