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SageMath
E = EllipticCurve("ft1")
E.isogeny_class()
Elliptic curves in class 212160.ft
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 212160.ft1 | 212160gc3 | \([0, 1, 0, -4903681, 4170818399]\) | \(49745123032831462081/97939634471640\) | \(25674287538933596160\) | \([2]\) | \(8847360\) | \(2.6124\) | |
| 212160.ft2 | 212160gc4 | \([0, 1, 0, -4110081, -3191910561]\) | \(29291056630578924481/175463302795560\) | \(45996652048039280640\) | \([2]\) | \(8847360\) | \(2.6124\) | |
| 212160.ft3 | 212160gc2 | \([0, 1, 0, -410881, 16775519]\) | \(29263955267177281/16463793153600\) | \(4315884592457318400\) | \([2, 2]\) | \(4423680\) | \(2.2658\) | |
| 212160.ft4 | 212160gc1 | \([0, 1, 0, 101119, 2132319]\) | \(436192097814719/259683840000\) | \(-68074560552960000\) | \([2]\) | \(2211840\) | \(1.9193\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 212160.ft have rank \(0\).
Complex multiplication
The elliptic curves in class 212160.ft do not have complex multiplication.Modular form 212160.2.a.ft
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
