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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 5586.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5586.l1 | 5586p2 | \([1, 0, 1, -41725, -12101680]\) | \(-1393520833033/10161910296\) | \(-58581390636291096\) | \([]\) | \(72576\) | \(1.9005\) | |
5586.l2 | 5586p1 | \([1, 0, 1, 4580, 419192]\) | \(1843623047/14211126\) | \(-81924313375926\) | \([3]\) | \(24192\) | \(1.3512\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5586.l have rank \(1\).
Complex multiplication
The elliptic curves in class 5586.l do not have complex multiplication.Modular form 5586.2.a.l
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.