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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 33066.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33066.h1 | 33066f2 | \([1, -1, 0, -3368592, 138683648]\) | \(156568813065172464046875/90302947539489980416\) | \(2438179583566229471232\) | \([2]\) | \(1302528\) | \(2.7933\) | |
| 33066.h2 | 33066f1 | \([1, -1, 0, -2385552, 1415259392]\) | \(55606647632008753582875/159430298424049664\) | \(4304618057449340928\) | \([2]\) | \(651264\) | \(2.4468\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 33066.h have rank \(1\).
Complex multiplication
The elliptic curves in class 33066.h do not have complex multiplication.Modular form 33066.2.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.
