Show commands:
SageMath
E = EllipticCurve("ev1")
E.isogeny_class()
Elliptic curves in class 346560ev
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
346560.ev2 | 346560ev1 | \([0, -1, 0, -5221985, 4730906337]\) | \(-186169411/6480\) | \(-548147372125826580480\) | \([2]\) | \(14008320\) | \(2.7524\) | \(\Gamma_0(N)\)-optimal |
346560.ev1 | 346560ev2 | \([0, -1, 0, -84237665, 297610425825]\) | \(781484460931/900\) | \(76131579461920358400\) | \([2]\) | \(28016640\) | \(3.0989\) |
Rank
sage: E.rank()
The elliptic curves in class 346560ev have rank \(0\).
Complex multiplication
The elliptic curves in class 346560ev do not have complex multiplication.Modular form 346560.2.a.ev
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.