Show commands:
SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 7098.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7098.x1 | 7098z1 | \([1, 0, 0, -1991077, -1081551199]\) | \(-82318551880501/54432\) | \(-577224109871136\) | \([]\) | \(156000\) | \(2.1494\) | \(\Gamma_0(N)\)-optimal |
7098.x2 | 7098z2 | \([1, 0, 0, 4105598, -5592345916]\) | \(721710134999099/1691848015872\) | \(-17941201223525918048256\) | \([]\) | \(780000\) | \(2.9541\) |
Rank
sage: E.rank()
The elliptic curves in class 7098.x have rank \(0\).
Complex multiplication
The elliptic curves in class 7098.x do not have complex multiplication.Modular form 7098.2.a.x
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.