Show commands:
SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 82810o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 82810.bj2 | 82810o1 | \([1, 1, 0, -588123, -204400867]\) | \(-115501303/25600\) | \(-4986346328321612800\) | \([2]\) | \(2580480\) | \(2.3082\) | \(\Gamma_0(N)\)-optimal |
| 82810.bj1 | 82810o2 | \([1, 1, 0, -9862843, -11925792003]\) | \(544737993463/20000\) | \(3895583069001260000\) | \([2]\) | \(5160960\) | \(2.6548\) |
Rank
sage: E.rank()
The elliptic curves in class 82810o have rank \(0\).
Complex multiplication
The elliptic curves in class 82810o do not have complex multiplication.Modular form 82810.2.a.o
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.
