Show commands:
SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 54150.bk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54150.bk1 | 54150t2 | \([1, 0, 1, -240818776, 1434737084198]\) | \(306331959547531/900000000\) | \(4537795750017187500000000\) | \([2]\) | \(28016640\) | \(3.6014\) | |
54150.bk2 | 54150t1 | \([1, 0, 1, -21330776, 1919420198]\) | \(212883113611/122880000\) | \(619560379735680000000000\) | \([2]\) | \(14008320\) | \(3.2548\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 54150.bk have rank \(0\).
Complex multiplication
The elliptic curves in class 54150.bk do not have complex multiplication.Modular form 54150.2.a.bk
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.