Show commands:
SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 9450.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9450.p1 | 9450c2 | \([1, -1, 0, -134757, -18511979]\) | \(44548516344270315/1322306994176\) | \(8033014989619200\) | \([]\) | \(77760\) | \(1.8288\) | |
9450.p2 | 9450c1 | \([1, -1, 0, -133782, -18800684]\) | \(392296847395243635/10976\) | \(7408800\) | \([]\) | \(25920\) | \(1.2795\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9450.p have rank \(1\).
Complex multiplication
The elliptic curves in class 9450.p do not have complex multiplication.Modular form 9450.2.a.p
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.