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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 8050d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8050.a2 | 8050d1 | \([1, 0, 1, -101, 348]\) | \(7189057/644\) | \(10062500\) | \([2]\) | \(3072\) | \(0.083456\) | \(\Gamma_0(N)\)-optimal |
8050.a1 | 8050d2 | \([1, 0, 1, -351, -2152]\) | \(304821217/51842\) | \(810031250\) | \([2]\) | \(6144\) | \(0.43003\) |
Rank
sage: E.rank()
The elliptic curves in class 8050d have rank \(1\).
Complex multiplication
The elliptic curves in class 8050d do not have complex multiplication.Modular form 8050.2.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.