Show commands:
SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 84966.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
84966.h1 | 84966x2 | \([1, 1, 0, -18489331186, -967682600103260]\) | \(717647917494305598319/844621814448\) | \(822693720401743999074661584\) | \([2]\) | \(130056192\) | \(4.4473\) | |
84966.h2 | 84966x1 | \([1, 1, 0, -1146071266, -15381541155980]\) | \(-170915990723796079/6015674034432\) | \(-5859494944900839815921139456\) | \([2]\) | \(65028096\) | \(4.1007\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 84966.h have rank \(0\).
Complex multiplication
The elliptic curves in class 84966.h do not have complex multiplication.Modular form 84966.2.a.h
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.