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SageMath
E = EllipticCurve("hx1")
E.isogeny_class()
Elliptic curves in class 100800.hx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 100800.hx1 | 100800eh2 | \([0, 0, 0, -5047500, 4618150000]\) | \(-7620530425/526848\) | \(-983224811520000000000\) | \([]\) | \(4976640\) | \(2.7791\) | |
| 100800.hx2 | 100800eh1 | \([0, 0, 0, 352500, 6550000]\) | \(2595575/1512\) | \(-2821754880000000000\) | \([]\) | \(1658880\) | \(2.2298\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 100800.hx have rank \(0\).
Complex multiplication
The elliptic curves in class 100800.hx do not have complex multiplication.Modular form 100800.2.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.
