Show commands:
SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 44100bz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
44100.t2 | 44100bz1 | \([0, 0, 0, -14700, -2786875]\) | \(-16384/147\) | \(-3151904946750000\) | \([2]\) | \(184320\) | \(1.6564\) | \(\Gamma_0(N)\)-optimal |
44100.t1 | 44100bz2 | \([0, 0, 0, -400575, -97326250]\) | \(20720464/63\) | \(21613062492000000\) | \([2]\) | \(368640\) | \(2.0030\) |
Rank
sage: E.rank()
The elliptic curves in class 44100bz have rank \(0\).
Complex multiplication
The elliptic curves in class 44100bz do not have complex multiplication.Modular form 44100.2.a.bz
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.