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SageMath
E = EllipticCurve("eo1")
E.isogeny_class()
Elliptic curves in class 414960.eo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
414960.eo1 | 414960eo2 | \([0, 1, 0, -155496, 23548980]\) | \(101513598260088169/377613600\) | \(1546705305600\) | \([2]\) | \(1597440\) | \(1.5546\) | \(\Gamma_0(N)\)-optimal* |
414960.eo2 | 414960eo1 | \([0, 1, 0, -9576, 376884]\) | \(-23711636464489/1513774080\) | \(-6200418631680\) | \([2]\) | \(798720\) | \(1.2080\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 414960.eo have rank \(0\).
Complex multiplication
The elliptic curves in class 414960.eo do not have complex multiplication.Modular form 414960.2.a.eo
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.