Show commands:
SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 142912bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
142912.k2 | 142912bj1 | \([0, 1, 0, -715401, 232673527]\) | \(-9885826857324297664/503815352887\) | \(-2063627685425152\) | \([2]\) | \(2531328\) | \(2.0086\) | \(\Gamma_0(N)\)-optimal |
142912.k1 | 142912bj2 | \([0, 1, 0, -11446561, 14902169247]\) | \(5061729074867291695688/13145671\) | \(430757347328\) | \([2]\) | \(5062656\) | \(2.3551\) |
Rank
sage: E.rank()
The elliptic curves in class 142912bj have rank \(1\).
Complex multiplication
The elliptic curves in class 142912bj do not have complex multiplication.Modular form 142912.2.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 Cremona 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 Cremona labels.