Show commands:
SageMath
E = EllipticCurve("fi1")
E.isogeny_class()
Elliptic curves in class 166464fi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 166464.ds2 | 166464fi1 | \([0, 0, 0, -86700, 7153328]\) | \(62500/17\) | \(19604235394547712\) | \([2]\) | \(884736\) | \(1.8341\) | \(\Gamma_0(N)\)-optimal |
| 166464.ds1 | 166464fi2 | \([0, 0, 0, -502860, -131511184]\) | \(6097250/289\) | \(666544003414622208\) | \([2]\) | \(1769472\) | \(2.1806\) |
Rank
sage: E.rank()
The elliptic curves in class 166464fi have rank \(0\).
Complex multiplication
The elliptic curves in class 166464fi do not have complex multiplication.Modular form 166464.2.a.fi
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.
