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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 5520.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5520.d1 | 5520l2 | \([0, -1, 0, -12576, 380160]\) | \(53706380371489/16171875000\) | \(66240000000000\) | \([2]\) | \(11520\) | \(1.3573\) | |
5520.d2 | 5520l1 | \([0, -1, 0, 2144, 38656]\) | \(265971760991/317400000\) | \(-1300070400000\) | \([2]\) | \(5760\) | \(1.0107\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5520.d have rank \(0\).
Complex multiplication
The elliptic curves in class 5520.d do not have complex multiplication.Modular form 5520.2.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.