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SageMath
E = EllipticCurve("fb1")
E.isogeny_class()
Elliptic curves in class 64350.fb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 64350.fb1 | 64350dy4 | \([1, -1, 1, -1373855, -619466353]\) | \(25176685646263969/57915000\) | \(659688046875000\) | \([2]\) | \(884736\) | \(2.0870\) | |
| 64350.fb2 | 64350dy2 | \([1, -1, 1, -86855, -9428353]\) | \(6361447449889/294465600\) | \(3354147225000000\) | \([2, 2]\) | \(442368\) | \(1.7405\) | |
| 64350.fb3 | 64350dy1 | \([1, -1, 1, -14855, 507647]\) | \(31824875809/8785920\) | \(100077120000000\) | \([4]\) | \(221184\) | \(1.3939\) | \(\Gamma_0(N)\)-optimal |
| 64350.fb4 | 64350dy3 | \([1, -1, 1, 48145, -36158353]\) | \(1083523132511/50179392120\) | \(-571574638366875000\) | \([2]\) | \(884736\) | \(2.0870\) |
Rank
sage: E.rank()
The elliptic curves in class 64350.fb have rank \(0\).
Complex multiplication
The elliptic curves in class 64350.fb do not have complex multiplication.Modular form 64350.2.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.
