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SageMath
sage: E = EllipticCurve("h1")
sage: E.isogeny_class()
Elliptic curves in class 62400.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 62400.h1 | 62400by2 | \([0, -1, 0, -14556833, -19692938463]\) | \(666276475992821/58199166792\) | \(29797973397504000000000\) | \([2]\) | \(5898240\) | \(3.0529\) | |
| 62400.h2 | 62400by1 | \([0, -1, 0, -14236833, -20671178463]\) | \(623295446073461/5458752\) | \(2794881024000000000\) | \([2]\) | \(2949120\) | \(2.7064\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 62400.h have rank \(1\).
Complex multiplication
The elliptic curves in class 62400.h do not have complex multiplication.Modular form 62400.2.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.
