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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 140790.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
140790.u1 | 140790ch2 | \([1, 0, 1, -16614, 736966]\) | \(10779215329/1232010\) | \(57960995850810\) | \([2]\) | \(628992\) | \(1.3732\) | |
140790.u2 | 140790ch1 | \([1, 0, 1, 1436, 58286]\) | \(6967871/35100\) | \(-1651310423100\) | \([2]\) | \(314496\) | \(1.0266\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 140790.u have rank \(0\).
Complex multiplication
The elliptic curves in class 140790.u do not have complex multiplication.Modular form 140790.2.a.u
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.