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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 397800l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
397800.l2 | 397800l1 | \([0, 0, 0, 68925, 3192750]\) | \(83824368372/58703125\) | \(-25359750000000000\) | \([2]\) | \(2580480\) | \(1.8362\) | \(\Gamma_0(N)\)-optimal |
397800.l1 | 397800l2 | \([0, 0, 0, -306075, 26817750]\) | \(3670232225814/1764381125\) | \(1524425292000000000\) | \([2]\) | \(5160960\) | \(2.1828\) |
Rank
sage: E.rank()
The elliptic curves in class 397800l have rank \(0\).
Complex multiplication
The elliptic curves in class 397800l do not have complex multiplication.Modular form 397800.2.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 Cremona 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 Cremona labels.