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SageMath
E = EllipticCurve("fb1")
E.isogeny_class()
Elliptic curves in class 46800fb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46800.e2 | 46800fb1 | \([0, 0, 0, -1162875, -7793750]\) | \(29819839301/17252352\) | \(100615716864000000000\) | \([2]\) | \(1720320\) | \(2.5276\) | \(\Gamma_0(N)\)-optimal |
| 46800.e1 | 46800fb2 | \([0, 0, 0, -12682875, 17329806250]\) | \(38686490446661/141927552\) | \(827721483264000000000\) | \([2]\) | \(3440640\) | \(2.8742\) |
Rank
sage: E.rank()
The elliptic curves in class 46800fb have rank \(2\).
Complex multiplication
The elliptic curves in class 46800fb do not have complex multiplication.Modular form 46800.2.a.fb
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.
