Show commands:
SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 107800bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 107800.g2 | 107800bu1 | \([0, 1, 0, -408, 3426688]\) | \(-4/2695\) | \(-5073024880000000\) | \([2]\) | \(589824\) | \(1.6924\) | \(\Gamma_0(N)\)-optimal |
| 107800.g1 | 107800bu2 | \([0, 1, 0, -343408, 76142688]\) | \(1189646642/21175\) | \(79718962400000000\) | \([2]\) | \(1179648\) | \(2.0390\) |
Rank
sage: E.rank()
The elliptic curves in class 107800bu have rank \(1\).
Complex multiplication
The elliptic curves in class 107800bu do not have complex multiplication.Modular form 107800.2.a.bu
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 Cremona 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 Cremona labels.
