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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 29040ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29040.d3 | 29040ci1 | \([0, -1, 0, -5001, 179676]\) | \(-488095744/200475\) | \(-5682459063600\) | \([2]\) | \(69120\) | \(1.1557\) | \(\Gamma_0(N)\)-optimal |
| 29040.d2 | 29040ci2 | \([0, -1, 0, -86676, 9849996]\) | \(158792223184/16335\) | \(7408242927360\) | \([2]\) | \(138240\) | \(1.5022\) | |
| 29040.d4 | 29040ci3 | \([0, -1, 0, 38559, -1959120]\) | \(223673040896/187171875\) | \(-5305382304750000\) | \([2]\) | \(207360\) | \(1.7050\) | |
| 29040.d1 | 29040ci4 | \([0, -1, 0, -188316, -17023620]\) | \(1628514404944/664335375\) | \(301289124165216000\) | \([2]\) | \(414720\) | \(2.0516\) |
Rank
sage: E.rank()
The elliptic curves in class 29040ci have rank \(1\).
Complex multiplication
The elliptic curves in class 29040ci do not have complex multiplication.Modular form 29040.2.a.ci
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.
