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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 4032.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4032.o1 | 4032s1 | \([0, 0, 0, -195, -1048]\) | \(474552000/49\) | \(84672\) | \([2]\) | \(512\) | \(-0.021869\) | \(\Gamma_0(N)\)-optimal |
4032.o2 | 4032s2 | \([0, 0, 0, -180, -1216]\) | \(-5832000/2401\) | \(-265531392\) | \([2]\) | \(1024\) | \(0.32470\) |
Rank
sage: E.rank()
The elliptic curves in class 4032.o have rank \(0\).
Complex multiplication
The elliptic curves in class 4032.o do not have complex multiplication.Modular form 4032.2.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.