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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 126852h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 126852.l2 | 126852h1 | \([0, 1, 0, 21783, 1270620]\) | \(80494592/95139\) | \(-1350979403306544\) | \([2]\) | \(645120\) | \(1.5896\) | \(\Gamma_0(N)\)-optimal |
| 126852.l1 | 126852h2 | \([0, 1, 0, -127172, 11995380]\) | \(1001132368/303831\) | \(69030689510889216\) | \([2]\) | \(1290240\) | \(1.9361\) |
Rank
sage: E.rank()
The elliptic curves in class 126852h have rank \(0\).
Complex multiplication
The elliptic curves in class 126852h do not have complex multiplication.Modular form 126852.2.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.
