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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 16830.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16830.f1 | 16830p1 | \([1, -1, 0, -21958515, -39645067019]\) | \(-1606220241149825308027441/2128704136908800000\) | \(-1551825315806515200000\) | \([]\) | \(1440000\) | \(2.9725\) | \(\Gamma_0(N)\)-optimal |
| 16830.f2 | 16830p2 | \([1, -1, 0, 155552085, 462972313741]\) | \(570983676137286216962798159/457469996554140806256680\) | \(-333495627487968647761119720\) | \([]\) | \(7200000\) | \(3.7772\) |
Rank
sage: E.rank()
The elliptic curves in class 16830.f have rank \(0\).
Complex multiplication
The elliptic curves in class 16830.f 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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
