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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 5440.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5440.r1 | 5440u2 | \([0, 1, 0, -425025, 109949375]\) | \(-32391289681150609/1228250000000\) | \(-321978368000000000\) | \([]\) | \(48384\) | \(2.1295\) | |
| 5440.r2 | 5440u1 | \([0, 1, 0, 25535, 496063]\) | \(7023836099951/4456448000\) | \(-1168231104512000\) | \([]\) | \(16128\) | \(1.5802\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5440.r have rank \(1\).
Complex multiplication
The elliptic curves in class 5440.r do not have complex multiplication.Modular form 5440.2.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 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.
