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SageMath
sage: E = EllipticCurve("n1")
sage: E.isogeny_class()
Elliptic curves in class 19600.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19600.n1 | 19600z2 | \([0, 1, 0, -294408, 43631188]\) | \(2185454/625\) | \(807072140000000000\) | \([2]\) | \(258048\) | \(2.1426\) | |
19600.n2 | 19600z1 | \([0, 1, 0, 48592, 4529188]\) | \(19652/25\) | \(-16141442800000000\) | \([2]\) | \(129024\) | \(1.7960\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 19600.n have rank \(0\).
Complex multiplication
The elliptic curves in class 19600.n do not have complex multiplication.Modular form 19600.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.