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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 254100.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 254100.h1 | 254100h2 | \([0, -1, 0, -1634508, 60427512]\) | \(68150496976/39220335\) | \(277924863571740000000\) | \([2]\) | \(9953280\) | \(2.6124\) | |
| 254100.h2 | 254100h1 | \([0, -1, 0, 407367, 7338762]\) | \(16880451584/9823275\) | \(-4350632720568750000\) | \([2]\) | \(4976640\) | \(2.2658\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 254100.h have rank \(1\).
Complex multiplication
The elliptic curves in class 254100.h do not have complex multiplication.Modular form 254100.2.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.
