Show commands:
SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 86190.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
86190.u1 | 86190bc2 | \([1, 0, 1, -4329784, -3380807818]\) | \(846509996114173/24354723600\) | \(258269651145788302800\) | \([2]\) | \(5271552\) | \(2.6948\) | |
86190.u2 | 86190bc1 | \([1, 0, 1, 64216, -174945418]\) | \(2761677827/1248480000\) | \(-13239505377203040000\) | \([2]\) | \(2635776\) | \(2.3482\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 86190.u have rank \(1\).
Complex multiplication
The elliptic curves in class 86190.u do not have complex multiplication.Modular form 86190.2.a.u
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.