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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 16830f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16830.i2 | 16830f1 | \([1, -1, 0, -9522645, 11099832821]\) | \(4851826120835540459523/104813489343692800\) | \(2063043910751905382400\) | \([2]\) | \(1128960\) | \(2.8785\) | \(\Gamma_0(N)\)-optimal |
| 16830.i1 | 16830f2 | \([1, -1, 0, -20581845, -19518668299]\) | \(48987507305640443781123/19983176659298631680\) | \(393328866184974967357440\) | \([2]\) | \(2257920\) | \(3.2251\) |
Rank
sage: E.rank()
The elliptic curves in class 16830f have rank \(0\).
Complex multiplication
The elliptic curves in class 16830f do not have complex multiplication.Modular form 16830.2.a.f
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.
