Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 68400.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
68400.g1 | 68400do2 | \([0, 0, 0, -1950075, 1038062250]\) | \(651038076963/7220000\) | \(9095120640000000000\) | \([2]\) | \(2211840\) | \(2.4522\) | |
68400.g2 | 68400do1 | \([0, 0, 0, -222075, -14289750]\) | \(961504803/486400\) | \(612723916800000000\) | \([2]\) | \(1105920\) | \(2.1056\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 68400.g have rank \(1\).
Complex multiplication
The elliptic curves in class 68400.g do not have complex multiplication.Modular form 68400.2.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.