Show commands:
SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 10830.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10830.x1 | 10830w2 | \([1, 1, 1, -242780, 27442577]\) | \(4904335099/1822500\) | \(588098329202227500\) | \([2]\) | \(145920\) | \(2.1096\) | |
10830.x2 | 10830w1 | \([1, 1, 1, -105600, -12943215]\) | \(403583419/10800\) | \(3485027136013200\) | \([2]\) | \(72960\) | \(1.7630\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10830.x have rank \(1\).
Complex multiplication
The elliptic curves in class 10830.x do not have complex multiplication.Modular form 10830.2.a.x
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.