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SageMath
E = EllipticCurve("cs1")
E.isogeny_class()
Elliptic curves in class 140790.cs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
140790.cs1 | 140790e2 | \([1, 0, 0, -307760, 65689440]\) | \(68523370149961/243360\) | \(11449085600160\) | \([2]\) | \(1140480\) | \(1.7241\) | |
140790.cs2 | 140790e1 | \([1, 0, 0, -18960, 1056000]\) | \(-16022066761/998400\) | \(-46970607590400\) | \([2]\) | \(570240\) | \(1.3775\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 140790.cs have rank \(0\).
Complex multiplication
The elliptic curves in class 140790.cs do not have complex multiplication.Modular form 140790.2.a.cs
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.