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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 7938.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7938.o1 | 7938l2 | \([1, -1, 0, -17943, -892963]\) | \(1876833/64\) | \(21785966991936\) | \([]\) | \(27216\) | \(1.3314\) | |
7938.o2 | 7938l1 | \([1, -1, 0, -2508, 48572]\) | \(415233/4\) | \(16810159716\) | \([3]\) | \(9072\) | \(0.78207\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7938.o have rank \(0\).
Complex multiplication
The elliptic curves in class 7938.o do not have complex multiplication.Modular form 7938.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.