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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 29760s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29760.bj4 | 29760s1 | \([0, -1, 0, 88895, -11475263]\) | \(296354077829711/387386634240\) | \(-101551081846210560\) | \([2]\) | \(276480\) | \(1.9492\) | \(\Gamma_0(N)\)-optimal |
| 29760.bj3 | 29760s2 | \([0, -1, 0, -545985, -111405375]\) | \(68663623745397169/19216056254400\) | \(5037373850753433600\) | \([2]\) | \(552960\) | \(2.2957\) | |
| 29760.bj2 | 29760s3 | \([0, -1, 0, -2537665, -1564435775]\) | \(-6894246873502147249/47925198774000\) | \(-12563303307411456000\) | \([2]\) | \(829440\) | \(2.4985\) | |
| 29760.bj1 | 29760s4 | \([0, -1, 0, -40670145, -99816583743]\) | \(28379906689597370652529/1357352437500\) | \(355821797376000000\) | \([2]\) | \(1658880\) | \(2.8450\) |
Rank
sage: E.rank()
The elliptic curves in class 29760s have rank \(1\).
Complex multiplication
The elliptic curves in class 29760s do not have complex multiplication.Modular form 29760.2.a.s
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
