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SageMath
E = EllipticCurve("cs1")
E.isogeny_class()
Elliptic curves in class 44352cs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 44352.x1 | 44352cs1 | \([0, 0, 0, -620724, -190243384]\) | \(-35431687725461248/440311012911\) | \(-328690409894009856\) | \([]\) | \(829440\) | \(2.1716\) | \(\Gamma_0(N)\)-optimal |
| 44352.x2 | 44352cs2 | \([0, 0, 0, 2159196, -972213496]\) | \(1491325446082364672/1410025768453071\) | \(-1052578596047143689216\) | \([]\) | \(2488320\) | \(2.7210\) |
Rank
sage: E.rank()
The elliptic curves in class 44352cs have rank \(0\).
Complex multiplication
The elliptic curves in class 44352cs do not have complex multiplication.Modular form 44352.2.a.cs
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.
