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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 58800.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
58800.l1 | 58800bg1 | \([0, -1, 0, -1147883, -472980738]\) | \(1950665639360512/492075\) | \(42195431250000\) | \([2]\) | \(552960\) | \(1.9894\) | \(\Gamma_0(N)\)-optimal |
58800.l2 | 58800bg2 | \([0, -1, 0, -1143508, -476769488]\) | \(-120527903507632/1937102445\) | \(-2657704554540000000\) | \([2]\) | \(1105920\) | \(2.3360\) |
Rank
sage: E.rank()
The elliptic curves in class 58800.l have rank \(0\).
Complex multiplication
The elliptic curves in class 58800.l do not have complex multiplication.Modular form 58800.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.