Show commands:
SageMath
E = EllipticCurve("dh1")
E.isogeny_class()
Elliptic curves in class 450800dh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
450800.dh2 | 450800dh1 | \([0, 0, 0, -72275, 8489250]\) | \(-22180932/3703\) | \(-6970467952000000\) | \([2]\) | \(1572864\) | \(1.7670\) | \(\Gamma_0(N)\)-optimal* |
450800.dh1 | 450800dh2 | \([0, 0, 0, -1199275, 505496250]\) | \(50668941906/1127\) | \(4242893536000000\) | \([2]\) | \(3145728\) | \(2.1136\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 450800dh have rank \(2\).
Complex multiplication
The elliptic curves in class 450800dh do not have complex multiplication.Modular form 450800.2.a.dh
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.