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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 59840.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 59840.h1 | 59840o1 | \([0, 1, 0, -1184645, -496216757]\) | \(179551401487197159424/193592864403125\) | \(198239093148800000\) | \([2]\) | \(952320\) | \(2.2349\) | \(\Gamma_0(N)\)-optimal |
| 59840.h2 | 59840o2 | \([0, 1, 0, -891825, -747280625]\) | \(-4787879231470062544/11941708603515625\) | \(-195652953760000000000\) | \([2]\) | \(1904640\) | \(2.5815\) |
Rank
sage: E.rank()
The elliptic curves in class 59840.h have rank \(1\).
Complex multiplication
The elliptic curves in class 59840.h do not have complex multiplication.Modular form 59840.2.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.
