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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 5550d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5550.b2 | 5550d1 | \([1, 1, 0, -25, 625]\) | \(-117649/11100\) | \(-173437500\) | \([2]\) | \(1920\) | \(0.26052\) | \(\Gamma_0(N)\)-optimal |
5550.b1 | 5550d2 | \([1, 1, 0, -1275, 16875]\) | \(14688124849/123210\) | \(1925156250\) | \([2]\) | \(3840\) | \(0.60709\) |
Rank
sage: E.rank()
The elliptic curves in class 5550d have rank \(1\).
Complex multiplication
The elliptic curves in class 5550d do not have complex multiplication.Modular form 5550.2.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.