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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 5544r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5544.y2 | 5544r1 | \([0, 0, 0, -30243, 2415310]\) | \(-4097989445764/1004475087\) | \(-749836634545152\) | \([2]\) | \(30720\) | \(1.5725\) | \(\Gamma_0(N)\)-optimal |
| 5544.y1 | 5544r2 | \([0, 0, 0, -509403, 139934230]\) | \(9791533777258802/427901859\) | \(638854052272128\) | \([2]\) | \(61440\) | \(1.9191\) |
Rank
sage: E.rank()
The elliptic curves in class 5544r have rank \(0\).
Complex multiplication
The elliptic curves in class 5544r do not have complex multiplication.Modular form 5544.2.a.r
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
