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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 1386.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1386.l1 | 1386k2 | \([1, -1, 1, -4223, -104561]\) | \(11422548526761/4312\) | \(3143448\) | \([2]\) | \(1536\) | \(0.59732\) | |
1386.l2 | 1386k1 | \([1, -1, 1, -263, -1601]\) | \(-2749884201/54208\) | \(-39517632\) | \([2]\) | \(768\) | \(0.25075\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1386.l have rank \(0\).
Complex multiplication
The elliptic curves in class 1386.l do not have complex multiplication.Modular form 1386.2.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.