Show commands:
SageMath
E = EllipticCurve("cv1")
E.isogeny_class()
Elliptic curves in class 286110.cv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
286110.cv1 | 286110cv2 | \([1, -1, 0, -2228244, -1574686000]\) | \(-2575296504243/765952000\) | \(-363903619511291904000\) | \([]\) | \(12441600\) | \(2.6596\) | |
286110.cv2 | 286110cv1 | \([1, -1, 0, 203691, 18015253]\) | \(1434104310933/1046272480\) | \(-681870802827630240\) | \([]\) | \(4147200\) | \(2.1103\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 286110.cv have rank \(0\).
Complex multiplication
The elliptic curves in class 286110.cv do not have complex multiplication.Modular form 286110.2.a.cv
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.