Show commands:
SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 2898.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2898.r1 | 2898o2 | \([1, -1, 1, -30119, -1750017]\) | \(4144806984356137/568114785504\) | \(414155678632416\) | \([2]\) | \(15360\) | \(1.5316\) | |
2898.r2 | 2898o1 | \([1, -1, 1, 3001, -147009]\) | \(4101378352343/15049939968\) | \(-10971406236672\) | \([2]\) | \(7680\) | \(1.1851\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2898.r have rank \(0\).
Complex multiplication
The elliptic curves in class 2898.r do not have complex multiplication.Modular form 2898.2.a.r
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.