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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 5440i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5440.l1 | 5440i1 | \([0, 0, 0, -112, 456]\) | \(151732224/85\) | \(87040\) | \([2]\) | \(768\) | \(-0.10497\) | \(\Gamma_0(N)\)-optimal |
5440.l2 | 5440i2 | \([0, 0, 0, -92, 624]\) | \(-5256144/7225\) | \(-118374400\) | \([2]\) | \(1536\) | \(0.24160\) |
Rank
sage: E.rank()
The elliptic curves in class 5440i have rank \(1\).
Complex multiplication
The elliptic curves in class 5440i do not have complex multiplication.Modular form 5440.2.a.i
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.