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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 3450.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3450.n1 | 3450p2 | \([1, 1, 1, -13007513, -18274618969]\) | \(-24923353462910020825/341398360424448\) | \(-3333968363520000000000\) | \([]\) | \(336960\) | \(2.9366\) | |
3450.n2 | 3450p1 | \([1, 1, 1, 576862, -125893969]\) | \(2173899265153175/1961845235712\) | \(-19158644880000000000\) | \([]\) | \(112320\) | \(2.3873\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3450.n have rank \(0\).
Complex multiplication
The elliptic curves in class 3450.n do not have complex multiplication.Modular form 3450.2.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.