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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 23184.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
23184.c1 | 23184g2 | \([0, 0, 0, -3387, -32870]\) | \(5756278756/2705927\) | \(2019963681792\) | \([2]\) | \(46080\) | \(1.0554\) | |
23184.c2 | 23184g1 | \([0, 0, 0, 753, -3890]\) | \(253012016/181447\) | \(-33862364928\) | \([2]\) | \(23040\) | \(0.70887\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 23184.c have rank \(0\).
Complex multiplication
The elliptic curves in class 23184.c do not have complex multiplication.Modular form 23184.2.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.