Show commands:
SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 309465.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
309465.q1 | 309465q2 | \([0, 0, 1, -199962, 34575572]\) | \(-303464448/1625\) | \(-4734909405178875\) | \([]\) | \(1568160\) | \(1.8523\) | |
309465.q2 | 309465q1 | \([0, 0, 1, 6348, 252465]\) | \(7077888/10985\) | \(-43906704497955\) | \([]\) | \(522720\) | \(1.3030\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 309465.q have rank \(0\).
Complex multiplication
The elliptic curves in class 309465.q do not have complex multiplication.Modular form 309465.2.a.q
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.