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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 20097d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
20097.h2 | 20097d1 | \([1, -1, 0, -20238, -4123729]\) | \(-46574399618739/347190316781\) | \(-6833747005200423\) | \([2]\) | \(107136\) | \(1.7214\) | \(\Gamma_0(N)\)-optimal |
20097.h1 | 20097d2 | \([1, -1, 0, -529593, -147863710]\) | \(834563889111074499/2244268390133\) | \(44173934722987839\) | \([2]\) | \(214272\) | \(2.0680\) |
Rank
sage: E.rank()
The elliptic curves in class 20097d have rank \(1\).
Complex multiplication
The elliptic curves in class 20097d do not have complex multiplication.Modular form 20097.2.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 Cremona 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 Cremona labels.