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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 50008.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 50008.h1 | 50008i1 | \([0, -1, 0, -84, 164]\) | \(259108432/118769\) | \(30404864\) | \([2]\) | \(9856\) | \(0.13070\) | \(\Gamma_0(N)\)-optimal |
| 50008.h2 | 50008i2 | \([0, -1, 0, 296, 924]\) | \(2791456412/2056579\) | \(-2105936896\) | \([2]\) | \(19712\) | \(0.47728\) |
Rank
sage: E.rank()
The elliptic curves in class 50008.h have rank \(1\).
Complex multiplication
The elliptic curves in class 50008.h do not have complex multiplication.Modular form 50008.2.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 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.
