Show commands:
SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 444675.bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
444675.bj1 | 444675bj2 | \([0, 1, 1, -3970997158, -1820911366584656]\) | \(-2126464142970105856/438611057788643355\) | \(-1428380634338483893179283728046875\) | \([]\) | \(4147200000\) | \(5.0411\) | |
444675.bj2 | 444675bj1 | \([0, 1, 1, -1325180908, 21744015290344]\) | \(-79028701534867456/16987307596875\) | \(-55320860635072475603466796875\) | \([]\) | \(829440000\) | \(4.2364\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 444675.bj have rank \(0\).
Complex multiplication
The elliptic curves in class 444675.bj do not have complex multiplication.Modular form 444675.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.