Show commands:
SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 48672.br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 48672.br1 | 48672br1 | \([0, 0, 0, -4414449, -3568903468]\) | \(42246001231552/14414517\) | \(3246143472741019968\) | \([2]\) | \(1032192\) | \(2.5236\) | \(\Gamma_0(N)\)-optimal |
| 48672.br2 | 48672br2 | \([0, 0, 0, -3798444, -4600342240]\) | \(-420526439488/390971529\) | \(-5634984461915670810624\) | \([2]\) | \(2064384\) | \(2.8702\) |
Rank
sage: E.rank()
The elliptic curves in class 48672.br have rank \(1\).
Complex multiplication
The elliptic curves in class 48672.br do not have complex multiplication.Modular form 48672.2.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.
