Show commands:
SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 302016bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
302016.bj1 | 302016bj1 | \([0, -1, 0, -1613, -10899]\) | \(256000/117\) | \(212247180288\) | \([2]\) | \(358400\) | \(0.86835\) | \(\Gamma_0(N)\)-optimal |
302016.bj2 | 302016bj2 | \([0, -1, 0, 5647, -87855]\) | \(686000/507\) | \(-14715804499968\) | \([2]\) | \(716800\) | \(1.2149\) |
Rank
sage: E.rank()
The elliptic curves in class 302016bj have rank \(1\).
Complex multiplication
The elliptic curves in class 302016bj do not have complex multiplication.Modular form 302016.2.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.