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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 49686.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
49686.l1 | 49686f2 | \([1, 1, 0, -42713570, 107429494866]\) | \(531373116625/2058\) | \(33378524410123496058\) | \([]\) | \(3773952\) | \(2.9595\) | |
49686.l2 | 49686f1 | \([1, 1, 0, -728900, 24312072]\) | \(2640625/1512\) | \(24522997525805017512\) | \([]\) | \(1257984\) | \(2.4102\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 49686.l have rank \(0\).
Complex multiplication
The elliptic curves in class 49686.l do not have complex multiplication.Modular form 49686.2.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.