Show commands:
SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 311696.bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 311696.bg1 | 311696bg2 | \([0, -1, 0, -29434984, -61457344144]\) | \(388686162930440257/734497456\) | \(5329744067169550336\) | \([]\) | \(18247680\) | \(2.8483\) | |
| 311696.bg2 | 311696bg1 | \([0, -1, 0, -472424, -29458064]\) | \(1606957644097/877735936\) | \(6369127434305929216\) | \([]\) | \(6082560\) | \(2.2989\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 311696.bg have rank \(1\).
Complex multiplication
The elliptic curves in class 311696.bg do not have complex multiplication.Modular form 311696.2.a.bg
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
