Show commands:
SageMath
E = EllipticCurve("ej1")
E.isogeny_class()
Elliptic curves in class 350658ej
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
350658.ej2 | 350658ej1 | \([1, -1, 1, 3244, 313679]\) | \(2924207/34776\) | \(-44912090089944\) | \([]\) | \(1382400\) | \(1.3005\) | \(\Gamma_0(N)\)-optimal |
350658.ej1 | 350658ej2 | \([1, -1, 1, -29426, -8860057]\) | \(-2181825073/25039686\) | \(-32337952422817734\) | \([]\) | \(4147200\) | \(1.8499\) |
Rank
sage: E.rank()
The elliptic curves in class 350658ej have rank \(1\).
Complex multiplication
The elliptic curves in class 350658ej do not have complex multiplication.Modular form 350658.2.a.ej
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.