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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 53900.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
53900.d1 | 53900p1 | \([0, 1, 0, -758, -8387]\) | \(-3937024/55\) | \(-673750000\) | \([]\) | \(31104\) | \(0.50001\) | \(\Gamma_0(N)\)-optimal |
53900.d2 | 53900p2 | \([0, 1, 0, 2742, -39887]\) | \(186050816/166375\) | \(-2038093750000\) | \([]\) | \(93312\) | \(1.0493\) |
Rank
sage: E.rank()
The elliptic curves in class 53900.d have rank \(1\).
Complex multiplication
The elliptic curves in class 53900.d do not have complex multiplication.Modular form 53900.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.