Show commands:
SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 297024n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 297024.n1 | 297024n1 | \([0, -1, 0, -4709, -122811]\) | \(11279816900608/1025661\) | \(1050276864\) | \([2]\) | \(245760\) | \(0.77027\) | \(\Gamma_0(N)\)-optimal |
| 297024.n2 | 297024n2 | \([0, -1, 0, -4369, -141647]\) | \(-563053038928/214121817\) | \(-3508171849728\) | \([2]\) | \(491520\) | \(1.1168\) |
Rank
sage: E.rank()
The elliptic curves in class 297024n have rank \(0\).
Complex multiplication
The elliptic curves in class 297024n do not have complex multiplication.Modular form 297024.2.a.n
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.
