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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 4998.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4998.c1 | 4998e2 | \([1, 1, 0, -1305651, 573689565]\) | \(717647917494305598319/844621814448\) | \(289705282355664\) | \([2]\) | \(64512\) | \(2.0577\) | |
4998.c2 | 4998e1 | \([1, 1, 0, -80931, 9093645]\) | \(-170915990723796079/6015674034432\) | \(-2063376193810176\) | \([2]\) | \(32256\) | \(1.7112\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4998.c have rank \(0\).
Complex multiplication
The elliptic curves in class 4998.c do not have complex multiplication.Modular form 4998.2.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.