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SageMath
E = EllipticCurve("el1")
E.isogeny_class()
Elliptic curves in class 388080.el
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388080.el1 | 388080el2 | \([0, 0, 0, -7295889888, -239864247039312]\) | \(1885935710810898432/4159375\) | \(94723932083138265600000\) | \([]\) | \(265628160\) | \(4.0816\) | |
| 388080.el2 | 388080el1 | \([0, 0, 0, -92889888, -307353239312]\) | \(2837428440956928/335693359375\) | \(10486893619125000000000000\) | \([]\) | \(88542720\) | \(3.5323\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 388080.el have rank \(0\).
Complex multiplication
The elliptic curves in class 388080.el do not have complex multiplication.Modular form 388080.2.a.el
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
