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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 236691h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 236691.h1 | 236691h1 | \([1, -1, 1, -121750697, -516979715840]\) | \(420100556152674123/62939003491\) | \(29902306122066052258857\) | \([2]\) | \(39813120\) | \(3.3260\) | \(\Gamma_0(N)\)-optimal |
| 236691.h2 | 236691h2 | \([1, -1, 1, -110475362, -616608575900]\) | \(-313859434290315003/164114213839849\) | \(-77970625351942688812315323\) | \([2]\) | \(79626240\) | \(3.6725\) |
Rank
sage: E.rank()
The elliptic curves in class 236691h have rank \(2\).
Complex multiplication
The elliptic curves in class 236691h do not have complex multiplication.Modular form 236691.2.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.
