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SageMath
E = EllipticCurve("hx1")
E.isogeny_class()
Elliptic curves in class 381150.hx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 381150.hx1 | 381150hx1 | \([1, -1, 0, -11598417, 15237946741]\) | \(-584043889/1400\) | \(-413620867934071875000\) | \([]\) | \(27371520\) | \(2.8353\) | \(\Gamma_0(N)\)-optimal |
| 381150.hx2 | 381150hx2 | \([1, -1, 0, 21343833, 76741127491]\) | \(3639707951/10718750\) | \(-3166784770120237792968750\) | \([]\) | \(82114560\) | \(3.3846\) |
Rank
sage: E.rank()
The elliptic curves in class 381150.hx have rank \(0\).
Complex multiplication
The elliptic curves in class 381150.hx do not have complex multiplication.Modular form 381150.2.a.hx
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
