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SageMath
E = EllipticCurve("cx1")
E.isogeny_class()
Elliptic curves in class 141120.cx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141120.cx1 | 141120he2 | \([0, 0, 0, -114828, -14976752]\) | \(68971442301/400\) | \(971086233600\) | \([2]\) | \(393216\) | \(1.4903\) | |
| 141120.cx2 | 141120he1 | \([0, 0, 0, -7308, -225008]\) | \(17779581/1280\) | \(3107475947520\) | \([2]\) | \(196608\) | \(1.1438\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 141120.cx have rank \(1\).
Complex multiplication
The elliptic curves in class 141120.cx do not have complex multiplication.Modular form 141120.2.a.cx
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.
