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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 4950h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4950.k3 | 4950h1 | \([1, -1, 0, -313542, 67654116]\) | \(299270638153369/1069200\) | \(12178856250000\) | \([2]\) | \(30720\) | \(1.7289\) | \(\Gamma_0(N)\)-optimal |
| 4950.k2 | 4950h2 | \([1, -1, 0, -318042, 65615616]\) | \(312341975961049/17862322500\) | \(203463017226562500\) | \([2, 2]\) | \(61440\) | \(2.0754\) | |
| 4950.k1 | 4950h3 | \([1, -1, 0, -936792, -266653134]\) | \(7981893677157049/1917731420550\) | \(21844159462202343750\) | \([2]\) | \(122880\) | \(2.4220\) | |
| 4950.k4 | 4950h4 | \([1, -1, 0, 228708, 267366366]\) | \(116149984977671/2779502343750\) | \(-31660268884277343750\) | \([2]\) | \(122880\) | \(2.4220\) |
Rank
sage: E.rank()
The elliptic curves in class 4950h have rank \(0\).
Complex multiplication
The elliptic curves in class 4950h do not have complex multiplication.Modular form 4950.2.a.h
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.
