Show commands:
SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 164730.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
164730.t1 | 164730cp2 | \([1, 1, 0, -3312, 71586]\) | \(818187429977/5343750\) | \(26253843750\) | \([2]\) | \(184320\) | \(0.83514\) | |
164730.t2 | 164730cp1 | \([1, 1, 0, -82, 2464]\) | \(-12649337/541500\) | \(-2660389500\) | \([2]\) | \(92160\) | \(0.48856\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 164730.t have rank \(2\).
Complex multiplication
The elliptic curves in class 164730.t do not have complex multiplication.Modular form 164730.2.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.