Show commands:
SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 12144.bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12144.bj1 | 12144be2 | \([0, 1, 0, -228, -936]\) | \(5142706000/1728243\) | \(442430208\) | \([2]\) | \(4608\) | \(0.36142\) | |
12144.bj2 | 12144be1 | \([0, 1, 0, -93, 306]\) | \(5619712000/184437\) | \(2950992\) | \([2]\) | \(2304\) | \(0.014845\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 12144.bj have rank \(0\).
Complex multiplication
The elliptic curves in class 12144.bj do not have complex multiplication.Modular form 12144.2.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.