Show commands:
SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 24255bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 24255.z2 | 24255bg1 | \([0, 0, 1, -588, -318047]\) | \(-262144/509355\) | \(-43685402561955\) | \([]\) | \(55296\) | \(1.2963\) | \(\Gamma_0(N)\)-optimal |
| 24255.z1 | 24255bg2 | \([0, 0, 1, -371028, -86991746]\) | \(-65860951343104/3493875\) | \(-299656106008875\) | \([]\) | \(165888\) | \(1.8456\) |
Rank
sage: E.rank()
The elliptic curves in class 24255bg have rank \(0\).
Complex multiplication
The elliptic curves in class 24255bg do not have complex multiplication.Modular form 24255.2.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 Cremona 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 Cremona labels.
