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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 44880.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
44880.n1 | 44880bm2 | \([0, -1, 0, -1836, 282540]\) | \(-2675089395664/132580078125\) | \(-33940500000000\) | \([]\) | \(124416\) | \(1.2763\) | |
44880.n2 | 44880bm1 | \([0, -1, 0, 204, -10404]\) | \(3649586096/182395125\) | \(-46693152000\) | \([]\) | \(41472\) | \(0.72696\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 44880.n have rank \(0\).
Complex multiplication
The elliptic curves in class 44880.n do not have complex multiplication.Modular form 44880.2.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.