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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 40432.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
40432.l1 | 40432j4 | \([0, 0, 0, -107939, 13649410]\) | \(1443468546/7\) | \(674449750016\) | \([2]\) | \(96768\) | \(1.4702\) | |
40432.l2 | 40432j3 | \([0, 0, 0, -21299, -946542]\) | \(11090466/2401\) | \(231336264255488\) | \([2]\) | \(96768\) | \(1.4702\) | |
40432.l3 | 40432j2 | \([0, 0, 0, -6859, 205770]\) | \(740772/49\) | \(2360574125056\) | \([2, 2]\) | \(48384\) | \(1.1236\) | |
40432.l4 | 40432j1 | \([0, 0, 0, 361, 13718]\) | \(432/7\) | \(-84306218752\) | \([2]\) | \(24192\) | \(0.77704\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 40432.l have rank \(1\).
Complex multiplication
The elliptic curves in class 40432.l do not have complex multiplication.Modular form 40432.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.