Show commands:
SageMath
E = EllipticCurve("dd1")
E.isogeny_class()
Elliptic curves in class 381150dd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
381150.dd1 | 381150dd1 | \([1, -1, 0, -6334917, 5675558741]\) | \(51603494067/4336640\) | \(2362766478644880000000\) | \([2]\) | \(22118400\) | \(2.8429\) | \(\Gamma_0(N)\)-optimal |
381150.dd2 | 381150dd2 | \([1, -1, 0, 6733083, 26048570741]\) | \(61958108493/573927200\) | \(-312697376158158337500000\) | \([2]\) | \(44236800\) | \(3.1895\) |
Rank
sage: E.rank()
The elliptic curves in class 381150dd have rank \(0\).
Complex multiplication
The elliptic curves in class 381150dd do not have complex multiplication.Modular form 381150.2.a.dd
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.