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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 2016.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2016.c1 | 2016a2 | \([0, 0, 0, -7020, 226368]\) | \(474552000/49\) | \(3950456832\) | \([2]\) | \(1536\) | \(0.87401\) | |
2016.c2 | 2016a1 | \([0, 0, 0, -405, 4104]\) | \(-5832000/2401\) | \(-3024568512\) | \([2]\) | \(768\) | \(0.52744\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2016.c have rank \(1\).
Complex multiplication
The elliptic curves in class 2016.c do not have complex multiplication.Modular form 2016.2.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.