Show commands:
SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 54978.bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54978.bj1 | 54978bl2 | \([1, 1, 1, -8919, -327909]\) | \(666940371553/37026\) | \(4356071874\) | \([2]\) | \(69120\) | \(0.91494\) | |
54978.bj2 | 54978bl1 | \([1, 1, 1, -589, -4705]\) | \(192100033/38148\) | \(4488074052\) | \([2]\) | \(34560\) | \(0.56837\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 54978.bj have rank \(1\).
Complex multiplication
The elliptic curves in class 54978.bj do not have complex multiplication.Modular form 54978.2.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.