Show commands:
SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 388080.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388080.x1 | 388080x3 | \([0, 0, 0, -7185961083, 207660178566218]\) | \(233632133015204766393938/29145526885986328125\) | \(5119383112729101562500000000000\) | \([2]\) | \(754974720\) | \(4.6222\) | |
| 388080.x2 | 388080x2 | \([0, 0, 0, -1794947763, -25909786333438]\) | \(7282213870869695463556/912102595400390625\) | \(80104961599000520490000000000\) | \([2, 2]\) | \(377487360\) | \(4.2756\) | |
| 388080.x3 | 388080x1 | \([0, 0, 0, -1737079743, -27865736983042]\) | \(26401417552259125806544/507547744790625\) | \(11143782731005405034400000\) | \([2]\) | \(188743680\) | \(3.9291\) | \(\Gamma_0(N)\)-optimal |
| 388080.x4 | 388080x4 | \([0, 0, 0, 2670177237, -134298909658438]\) | \(11986661998777424518222/51295853620928503125\) | \(-9010066203547324685040902400000\) | \([2]\) | \(754974720\) | \(4.6222\) |
Rank
sage: E.rank()
The elliptic curves in class 388080.x have rank \(1\).
Complex multiplication
The elliptic curves in class 388080.x do not have complex multiplication.Modular form 388080.2.a.x
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.
