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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 126960.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 126960.o1 | 126960a2 | \([0, -1, 0, -274403056, 1749658698400]\) | \(7536914291382802562/17961229575\) | \(5445440691544508774400\) | \([2]\) | \(22302720\) | \(3.4122\) | |
| 126960.o2 | 126960a1 | \([0, -1, 0, -16949336, 28014182016]\) | \(-3552342505518244/179863605135\) | \(-27265299133342402575360\) | \([2]\) | \(11151360\) | \(3.0656\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 126960.o have rank \(0\).
Complex multiplication
The elliptic curves in class 126960.o do not have complex multiplication.Modular form 126960.2.a.o
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
