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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 144150cc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 144150.dh3 | 144150cc1 | \([1, 1, 1, -2607213, 1439514531]\) | \(141339344329/17141760\) | \(237708985919040000000\) | \([4]\) | \(6635520\) | \(2.6403\) | \(\Gamma_0(N)\)-optimal |
| 144150.dh2 | 144150cc2 | \([1, 1, 1, -10295213, -11214933469]\) | \(8702409880009/1120910400\) | \(15543939157362225000000\) | \([2, 2]\) | \(13271040\) | \(2.9869\) | |
| 144150.dh4 | 144150cc3 | \([1, 1, 1, 15651787, -58594155469]\) | \(30579142915511/124675335000\) | \(-1728903417850127109375000\) | \([2]\) | \(26542080\) | \(3.3334\) | |
| 144150.dh1 | 144150cc4 | \([1, 1, 1, -159250213, -773566623469]\) | \(32208729120020809/658986840\) | \(9138331972352469375000\) | \([2]\) | \(26542080\) | \(3.3334\) |
Rank
sage: E.rank()
The elliptic curves in class 144150cc have rank \(1\).
Complex multiplication
The elliptic curves in class 144150cc do not have complex multiplication.Modular form 144150.2.a.cc
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.
