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SageMath
E = EllipticCurve("ow1")
E.isogeny_class()
Elliptic curves in class 273600ow
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 273600.ow4 | 273600ow1 | \([0, 0, 0, -27360300, 57571522000]\) | \(-758575480593601/40535043840\) | \(-121036992345538560000000\) | \([2]\) | \(35389440\) | \(3.1881\) | \(\Gamma_0(N)\)-optimal |
| 273600.ow3 | 273600ow2 | \([0, 0, 0, -443232300, 3591651778000]\) | \(3225005357698077121/8526675600\) | \(25460516914790400000000\) | \([2, 2]\) | \(70778880\) | \(3.5347\) | |
| 273600.ow1 | 273600ow3 | \([0, 0, 0, -7091712300, 229866020098000]\) | \(13209596798923694545921/92340\) | \(275725762560000000\) | \([2]\) | \(141557760\) | \(3.8812\) | |
| 273600.ow2 | 273600ow4 | \([0, 0, 0, -448704300, 3498419842000]\) | \(3345930611358906241/165622259047500\) | \(494545415559690240000000000\) | \([2]\) | \(141557760\) | \(3.8812\) |
Rank
sage: E.rank()
The elliptic curves in class 273600ow have rank \(0\).
Complex multiplication
The elliptic curves in class 273600ow do not have complex multiplication.Modular form 273600.2.a.ow
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.
