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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 41280h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 41280.t2 | 41280h1 | \([0, -1, 0, 159, -2079]\) | \(1685159/7740\) | \(-2028994560\) | \([2]\) | \(21504\) | \(0.46830\) | \(\Gamma_0(N)\)-optimal |
| 41280.t1 | 41280h2 | \([0, -1, 0, -1761, -24735]\) | \(2305199161/277350\) | \(72705638400\) | \([2]\) | \(43008\) | \(0.81487\) |
Rank
sage: E.rank()
The elliptic curves in class 41280h have rank \(1\).
Complex multiplication
The elliptic curves in class 41280h do not have complex multiplication.Modular form 41280.2.a.h
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.
