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SageMath
E = EllipticCurve("cu1")
E.isogeny_class()
Elliptic curves in class 130050.cu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 130050.cu1 | 130050fv3 | \([1, -1, 0, -48802617, 99222002541]\) | \(46753267515625/11591221248\) | \(3186913516326162432000000\) | \([2]\) | \(23887872\) | \(3.4121\) | |
| 130050.cu2 | 130050fv1 | \([1, -1, 0, -16615242, -26054187084]\) | \(1845026709625/793152\) | \(218070794717793000000\) | \([2]\) | \(7962624\) | \(2.8628\) | \(\Gamma_0(N)\)-optimal |
| 130050.cu3 | 130050fv2 | \([1, -1, 0, -14014242, -34489230084]\) | \(-1107111813625/1228691592\) | \(-337818919867201081125000\) | \([2]\) | \(15925248\) | \(3.2093\) | |
| 130050.cu4 | 130050fv4 | \([1, -1, 0, 117661383, 629076914541]\) | \(655215969476375/1001033261568\) | \(-275226083889441258312000000\) | \([2]\) | \(47775744\) | \(3.7586\) |
Rank
sage: E.rank()
The elliptic curves in class 130050.cu have rank \(0\).
Complex multiplication
The elliptic curves in class 130050.cu do not have complex multiplication.Modular form 130050.2.a.cu
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
