Show commands:
SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 69828.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
69828.t1 | 69828i2 | \([0, -1, 0, -5406556, 4814954728]\) | \(461188987116496/2811467307\) | \(106546703919662316288\) | \([2]\) | \(3041280\) | \(2.6817\) | |
69828.t2 | 69828i1 | \([0, -1, 0, -5398621, 4829856658]\) | \(7346581704933376/275517\) | \(652582464473808\) | \([2]\) | \(1520640\) | \(2.3351\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 69828.t have rank \(1\).
Complex multiplication
The elliptic curves in class 69828.t do not have complex multiplication.Modular form 69828.2.a.t
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.