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SageMath
E = EllipticCurve("jx1")
E.isogeny_class()
Elliptic curves in class 141120.jx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141120.jx1 | 141120o2 | \([0, 0, 0, -13858572, 19858344464]\) | \(-5452947409/250\) | \(-13495465182560256000\) | \([]\) | \(5806080\) | \(2.7464\) | |
141120.jx2 | 141120o1 | \([0, 0, 0, -28812, 70723856]\) | \(-49/40\) | \(-2159274429209640960\) | \([]\) | \(1935360\) | \(2.1971\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 141120.jx have rank \(1\).
Complex multiplication
The elliptic curves in class 141120.jx do not have complex multiplication.Modular form 141120.2.a.jx
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.