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SageMath
E = EllipticCurve("cw1")
E.isogeny_class()
Elliptic curves in class 193550.cw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 193550.cw1 | 193550bk3 | \([1, 0, 0, -6390238, 6217073092]\) | \(15698803397448457/20709376\) | \(38069334016000000\) | \([]\) | \(4898880\) | \(2.4575\) | |
| 193550.cw2 | 193550bk2 | \([1, 0, 0, -99863, 3634217]\) | \(59914169497/31554496\) | \(58005545311000000\) | \([]\) | \(1632960\) | \(1.9082\) | |
| 193550.cw3 | 193550bk1 | \([1, 0, 0, -56988, -5240908]\) | \(11134383337/316\) | \(580891937500\) | \([]\) | \(544320\) | \(1.3589\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 193550.cw have rank \(0\).
Complex multiplication
The elliptic curves in class 193550.cw do not have complex multiplication.Modular form 193550.2.a.cw
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
