Show commands:
SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 85680.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
85680.n1 | 85680n2 | \([0, 0, 0, -74703, -7502402]\) | \(247041745675216/12672223725\) | \(2364941080454400\) | \([2]\) | \(491520\) | \(1.7078\) | |
85680.n2 | 85680n1 | \([0, 0, 0, -73758, -7710113]\) | \(3804552637966336/10833165\) | \(126358036560\) | \([2]\) | \(245760\) | \(1.3613\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 85680.n have rank \(0\).
Complex multiplication
The elliptic curves in class 85680.n do not have complex multiplication.Modular form 85680.2.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 LMFDB 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 LMFDB labels.