Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 361998.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
361998.g1 | 361998g2 | \([1, -1, 0, -107372238, -427947683500]\) | \(1440948051852717771/1029307365632\) | \(97790459516161537192704\) | \([2]\) | \(55738368\) | \(3.3469\) | |
361998.g2 | 361998g1 | \([1, -1, 0, -8081358, -3757185964]\) | \(614363455856331/291276783616\) | \(27673065856969569533952\) | \([2]\) | \(27869184\) | \(3.0003\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 361998.g have rank \(1\).
Complex multiplication
The elliptic curves in class 361998.g do not have complex multiplication.Modular form 361998.2.a.g
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.