Show commands:
SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 44352.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
44352.y1 | 44352cw1 | \([0, 0, 0, -19116, -1016496]\) | \(598885164/539\) | \(695280402432\) | \([2]\) | \(86016\) | \(1.1967\) | \(\Gamma_0(N)\)-optimal |
44352.y2 | 44352cw2 | \([0, 0, 0, -14796, -1488240]\) | \(-138853062/290521\) | \(-749512273821696\) | \([2]\) | \(172032\) | \(1.5433\) |
Rank
sage: E.rank()
The elliptic curves in class 44352.y have rank \(2\).
Complex multiplication
The elliptic curves in class 44352.y do not have complex multiplication.Modular form 44352.2.a.y
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.