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SageMath
E = EllipticCurve("cx1")
E.isogeny_class()
Elliptic curves in class 29400cx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29400.cd3 | 29400cx1 | \([0, -1, 0, -387508, 92971012]\) | \(13674725584/945\) | \(444713220000000\) | \([4]\) | \(221184\) | \(1.8644\) | \(\Gamma_0(N)\)-optimal |
| 29400.cd2 | 29400cx2 | \([0, -1, 0, -412008, 80574012]\) | \(4108974916/893025\) | \(1681015971600000000\) | \([2, 2]\) | \(442368\) | \(2.2110\) | |
| 29400.cd4 | 29400cx3 | \([0, -1, 0, 910992, 490704012]\) | \(22208984782/40516875\) | \(-152536634460000000000\) | \([2]\) | \(884736\) | \(2.5576\) | |
| 29400.cd1 | 29400cx4 | \([0, -1, 0, -2127008, -1123355988]\) | \(282678688658/18600435\) | \(70026322474080000000\) | \([2]\) | \(884736\) | \(2.5576\) |
Rank
sage: E.rank()
The elliptic curves in class 29400cx have rank \(1\).
Complex multiplication
The elliptic curves in class 29400cx do not have complex multiplication.Modular form 29400.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
