Show commands:
SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 389376.y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 389376.y1 | 389376y2 | \([0, 0, 0, -9477858, -11230870664]\) | \(-23788477376\) | \(-3958108181973504\) | \([]\) | \(7488000\) | \(2.4782\) | |
| 389376.y2 | 389376y1 | \([0, 0, 0, 13182, -2970344]\) | \(64\) | \(-3958108181973504\) | \([]\) | \(1497600\) | \(1.6735\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 389376.y have rank \(1\).
Complex multiplication
The elliptic curves in class 389376.y do not have complex multiplication.Modular form 389376.2.a.y
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.
