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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 116242.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
116242.o1 | 116242x2 | \([1, 0, 0, -218593, -36845751]\) | \(24553362849625/1755162752\) | \(82573177966224512\) | \([2]\) | \(1467648\) | \(1.9930\) | |
116242.o2 | 116242x1 | \([1, 0, 0, 12447, -2513207]\) | \(4533086375/60669952\) | \(-2854271342067712\) | \([2]\) | \(733824\) | \(1.6464\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 116242.o have rank \(0\).
Complex multiplication
The elliptic curves in class 116242.o do not have complex multiplication.Modular form 116242.2.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.