Show commands:
SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 119952.br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 119952.br1 | 119952j2 | \([0, 0, 0, -231, -490]\) | \(574992/289\) | \(685165824\) | \([2]\) | \(36864\) | \(0.38813\) | |
| 119952.br2 | 119952j1 | \([0, 0, 0, -126, 539]\) | \(1492992/17\) | \(2518992\) | \([2]\) | \(18432\) | \(0.041555\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 119952.br have rank \(1\).
Complex multiplication
The elliptic curves in class 119952.br do not have complex multiplication.Modular form 119952.2.a.br
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.
