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SageMath
E = EllipticCurve("hj1")
E.isogeny_class()
Elliptic curves in class 250800hj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 250800.hj2 | 250800hj1 | \([0, 1, 0, -145333, 22940963]\) | \(-5304438784000/497763387\) | \(-31856856768000000\) | \([]\) | \(1866240\) | \(1.9087\) | \(\Gamma_0(N)\)-optimal |
| 250800.hj1 | 250800hj2 | \([0, 1, 0, -12025333, 16046684963]\) | \(-3004935183806464000/2037123\) | \(-130375872000000\) | \([]\) | \(5598720\) | \(2.4580\) |
Rank
sage: E.rank()
The elliptic curves in class 250800hj have rank \(1\).
Complex multiplication
The elliptic curves in class 250800hj do not have complex multiplication.Modular form 250800.2.a.hj
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
