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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 10878.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10878.x1 | 10878bd2 | \([1, 1, 1, -116964, 15347877]\) | \(1504154129818033/5519808\) | \(649399891392\) | \([2]\) | \(46080\) | \(1.4830\) | |
10878.x2 | 10878bd1 | \([1, 1, 1, -7204, 244901]\) | \(-351447414193/22278144\) | \(-2621001363456\) | \([2]\) | \(23040\) | \(1.1365\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10878.x have rank \(1\).
Complex multiplication
The elliptic curves in class 10878.x do not have complex multiplication.Modular form 10878.2.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.