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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 2093.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2093.d1 | 2093d2 | \([1, 1, 1, -98, -296]\) | \(104154702625/32188247\) | \(32188247\) | \([2]\) | \(480\) | \(0.14515\) | |
2093.d2 | 2093d1 | \([1, 1, 1, 17, -20]\) | \(541343375/625807\) | \(-625807\) | \([2]\) | \(240\) | \(-0.20142\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2093.d have rank \(0\).
Complex multiplication
The elliptic curves in class 2093.d do not have complex multiplication.Modular form 2093.2.a.d
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.