Show commands:
SageMath
E = EllipticCurve("gx1")
E.isogeny_class()
Elliptic curves in class 176400gx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
176400.th2 | 176400gx1 | \([0, 0, 0, -255675, 49396970]\) | \(505318200625/4251528\) | \(15551368364851200\) | \([]\) | \(1658880\) | \(1.9324\) | \(\Gamma_0(N)\)-optimal |
176400.th1 | 176400gx2 | \([0, 0, 0, -20667675, 36164756810]\) | \(266916252066900625/162\) | \(592568524800\) | \([]\) | \(4976640\) | \(2.4817\) |
Rank
sage: E.rank()
The elliptic curves in class 176400gx have rank \(0\).
Complex multiplication
The elliptic curves in class 176400gx do not have complex multiplication.Modular form 176400.2.a.gx
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.