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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 64400.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
64400.d1 | 64400e1 | \([0, 1, 0, -1008, -2012]\) | \(7086244/4025\) | \(64400000000\) | \([2]\) | \(49152\) | \(0.76392\) | \(\Gamma_0(N)\)-optimal |
64400.d2 | 64400e2 | \([0, 1, 0, 3992, -12012]\) | \(219804478/129605\) | \(-4147360000000\) | \([2]\) | \(98304\) | \(1.1105\) |
Rank
sage: E.rank()
The elliptic curves in class 64400.d have rank \(1\).
Complex multiplication
The elliptic curves in class 64400.d do not have complex multiplication.Modular form 64400.2.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.