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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 41140.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 41140.j1 | 41140a1 | \([0, 0, 0, -3388, -75867]\) | \(151732224/85\) | \(2409322960\) | \([2]\) | \(33600\) | \(0.74740\) | \(\Gamma_0(N)\)-optimal |
| 41140.j2 | 41140a2 | \([0, 0, 0, -2783, -103818]\) | \(-5256144/7225\) | \(-3276679225600\) | \([2]\) | \(67200\) | \(1.0940\) |
Rank
sage: E.rank()
The elliptic curves in class 41140.j have rank \(1\).
Complex multiplication
The elliptic curves in class 41140.j do not have complex multiplication.Modular form 41140.2.a.j
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.
