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SageMath
E = EllipticCurve("ee1")
E.isogeny_class()
Elliptic curves in class 289800.ee
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 289800.ee1 | 289800ee1 | \([0, 0, 0, -237491175, -1356875351750]\) | \(508017439289666674384/21234429931640625\) | \(61919597680664062500000000\) | \([2]\) | \(82575360\) | \(3.7139\) | \(\Gamma_0(N)\)-optimal |
| 289800.ee2 | 289800ee2 | \([0, 0, 0, 114071325, -5031055039250]\) | \(14073614784514581404/945607964406328125\) | \(-11029571296835411250000000000\) | \([2]\) | \(165150720\) | \(4.0604\) |
Rank
sage: E.rank()
The elliptic curves in class 289800.ee have rank \(0\).
Complex multiplication
The elliptic curves in class 289800.ee do not have complex multiplication.Modular form 289800.2.a.ee
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.
