Show commands:
SageMath
E = EllipticCurve("go1")
E.isogeny_class()
Elliptic curves in class 217800go
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
217800.t2 | 217800go1 | \([0, 0, 0, -408375, 224606250]\) | \(-432\) | \(-17434817581500000000\) | \([2]\) | \(4915200\) | \(2.3805\) | \(\Gamma_0(N)\)-optimal |
217800.t1 | 217800go2 | \([0, 0, 0, -8575875, 9658068750]\) | \(1000188\) | \(69739270326000000000\) | \([2]\) | \(9830400\) | \(2.7270\) |
Rank
sage: E.rank()
The elliptic curves in class 217800go have rank \(1\).
Complex multiplication
The elliptic curves in class 217800go do not have complex multiplication.Modular form 217800.2.a.go
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.