Show commands:
SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 10710.bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10710.bj1 | 10710bm2 | \([1, -1, 1, -4667, -89229]\) | \(15417797707369/4080067320\) | \(2974369076280\) | \([2]\) | \(18432\) | \(1.1020\) | |
| 10710.bj2 | 10710bm1 | \([1, -1, 1, 733, -9309]\) | \(59822347031/83966400\) | \(-61211505600\) | \([2]\) | \(9216\) | \(0.75542\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10710.bj have rank \(1\).
Complex multiplication
The elliptic curves in class 10710.bj do not have complex multiplication.Modular form 10710.2.a.bj
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.
