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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 4620.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4620.n1 | 4620n1 | \([0, 1, 0, -2245, 83975]\) | \(-4890195460096/9282994875\) | \(-2376446688000\) | \([3]\) | \(7776\) | \(1.0645\) | \(\Gamma_0(N)\)-optimal |
4620.n2 | 4620n2 | \([0, 1, 0, 19355, -1788745]\) | \(3132137615458304/7250937873795\) | \(-1856240095691520\) | \([]\) | \(23328\) | \(1.6138\) |
Rank
sage: E.rank()
The elliptic curves in class 4620.n have rank \(1\).
Complex multiplication
The elliptic curves in class 4620.n do not have complex multiplication.Modular form 4620.2.a.n
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.