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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 104742.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
104742.o1 | 104742b2 | \([1, -1, 0, -916276767, -10663288182415]\) | \(29197483936393921875/37902516876004\) | \(110439989929933766845424748\) | \([2]\) | \(56770560\) | \(3.9044\) | |
104742.o2 | 104742b1 | \([1, -1, 0, -915991107, -10670276625787]\) | \(29170184477654905875/49252016\) | \(143510051558412574992\) | \([2]\) | \(28385280\) | \(3.5578\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 104742.o have rank \(0\).
Complex multiplication
The elliptic curves in class 104742.o do not have complex multiplication.Modular form 104742.2.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.