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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 5586e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5586.k2 | 5586e1 | \([1, 1, 0, 94, -1182]\) | \(1843623047/14211126\) | \(-696345174\) | \([]\) | \(3456\) | \(0.37827\) | \(\Gamma_0(N)\)-optimal |
5586.k1 | 5586e2 | \([1, 1, 0, -851, 34917]\) | \(-1393520833033/10161910296\) | \(-497933604504\) | \([]\) | \(10368\) | \(0.92758\) |
Rank
sage: E.rank()
The elliptic curves in class 5586e have rank \(0\).
Complex multiplication
The elliptic curves in class 5586e do not have complex multiplication.Modular form 5586.2.a.e
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.