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SageMath
E = EllipticCurve("fl1")
E.isogeny_class()
Elliptic curves in class 166464.fl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 166464.fl1 | 166464fy3 | \([0, 0, 0, -15096204, 22576138992]\) | \(82483294977/17\) | \(78416941578190848\) | \([2]\) | \(4718592\) | \(2.6290\) | |
| 166464.fl2 | 166464fy2 | \([0, 0, 0, -946764, 350198640]\) | \(20346417/289\) | \(1333088006829244416\) | \([2, 2]\) | \(2359296\) | \(2.2824\) | |
| 166464.fl3 | 166464fy1 | \([0, 0, 0, -114444, -6367248]\) | \(35937/17\) | \(78416941578190848\) | \([2]\) | \(1179648\) | \(1.9359\) | \(\Gamma_0(N)\)-optimal |
| 166464.fl4 | 166464fy4 | \([0, 0, 0, -114444, 944475120]\) | \(-35937/83521\) | \(-385262433973651636224\) | \([2]\) | \(4718592\) | \(2.6290\) |
Rank
sage: E.rank()
The elliptic curves in class 166464.fl have rank \(0\).
Complex multiplication
The elliptic curves in class 166464.fl do not have complex multiplication.Modular form 166464.2.a.fl
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.
