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SageMath
E = EllipticCurve("fb1")
E.isogeny_class()
Elliptic curves in class 33600.fb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33600.fb1 | 33600ge4 | \([0, 1, 0, -173633, -26275137]\) | \(282678688658/18600435\) | \(38093690880000000\) | \([2]\) | \(294912\) | \(1.9312\) | |
| 33600.fb2 | 33600ge2 | \([0, 1, 0, -33633, 1864863]\) | \(4108974916/893025\) | \(914457600000000\) | \([2, 2]\) | \(147456\) | \(1.5846\) | |
| 33600.fb3 | 33600ge1 | \([0, 1, 0, -31633, 2154863]\) | \(13674725584/945\) | \(241920000000\) | \([2]\) | \(73728\) | \(1.2380\) | \(\Gamma_0(N)\)-optimal |
| 33600.fb4 | 33600ge3 | \([0, 1, 0, 74367, 11476863]\) | \(22208984782/40516875\) | \(-82978560000000000\) | \([2]\) | \(294912\) | \(1.9312\) |
Rank
sage: E.rank()
The elliptic curves in class 33600.fb have rank \(1\).
Complex multiplication
The elliptic curves in class 33600.fb do not have complex multiplication.Modular form 33600.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
