Show commands:
SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 440440cb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
440440.cb1 | 440440cb1 | \([0, -1, 0, -435156, -110217820]\) | \(20093868785104/26374985\) | \(11961573069205760\) | \([2]\) | \(5376000\) | \(1.9917\) | \(\Gamma_0(N)\)-optimal |
440440.cb2 | 440440cb2 | \([0, -1, 0, -316576, -171737124]\) | \(-1934207124196/5912841025\) | \(-10726357564508185600\) | \([2]\) | \(10752000\) | \(2.3383\) |
Rank
sage: E.rank()
The elliptic curves in class 440440cb have rank \(1\).
Complex multiplication
The elliptic curves in class 440440cb do not have complex multiplication.Modular form 440440.2.a.cb
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.