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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 74704h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 74704.q2 | 74704h1 | \([0, -1, 0, 616, 20720]\) | \(6300872423/49827568\) | \(-204093718528\) | \([2]\) | \(61440\) | \(0.85161\) | \(\Gamma_0(N)\)-optimal |
| 74704.q1 | 74704h2 | \([0, -1, 0, -8664, 287984]\) | \(17561807821657/1590616244\) | \(6515164135424\) | \([2]\) | \(122880\) | \(1.1982\) |
Rank
sage: E.rank()
The elliptic curves in class 74704h have rank \(0\).
Complex multiplication
The elliptic curves in class 74704h do not have complex multiplication.Modular form 74704.2.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.
