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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 369600.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.x1 | 369600x2 | \([0, -1, 0, -91833, 5556537]\) | \(10706185664/4546773\) | \(36374184000000000\) | \([2]\) | \(3686400\) | \(1.8744\) | |
| 369600.x2 | 369600x1 | \([0, -1, 0, -43708, -3442838]\) | \(73876521536/1440747\) | \(180093375000000\) | \([2]\) | \(1843200\) | \(1.5278\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 369600.x have rank \(1\).
Complex multiplication
The elliptic curves in class 369600.x do not have complex multiplication.Modular form 369600.2.a.x
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
