Show commands:
SageMath
E = EllipticCurve("ct1")
E.isogeny_class()
Elliptic curves in class 9408ct
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9408.cr2 | 9408ct1 | \([0, 1, 0, -65, 447]\) | \(-2401/6\) | \(-77070336\) | \([]\) | \(2304\) | \(0.20124\) | \(\Gamma_0(N)\)-optimal |
9408.cr1 | 9408ct2 | \([0, 1, 0, -9025, -345409]\) | \(-6329617441/279936\) | \(-3595793596416\) | \([]\) | \(16128\) | \(1.1742\) |
Rank
sage: E.rank()
The elliptic curves in class 9408ct have rank \(0\).
Complex multiplication
The elliptic curves in class 9408ct do not have complex multiplication.Modular form 9408.2.a.ct
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.