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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 30492n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30492.t4 | 30492n1 | \([0, 0, 0, 7260, -81191]\) | \(2048000/1323\) | \(-27337793967792\) | \([2]\) | \(51840\) | \(1.2672\) | \(\Gamma_0(N)\)-optimal |
30492.t3 | 30492n2 | \([0, 0, 0, -30855, -668162]\) | \(9826000/5103\) | \(1687132427726592\) | \([2]\) | \(103680\) | \(1.6138\) | |
30492.t2 | 30492n3 | \([0, 0, 0, -123420, -17187203]\) | \(-10061824000/352947\) | \(-7293115924074288\) | \([2]\) | \(155520\) | \(1.8165\) | |
30492.t1 | 30492n4 | \([0, 0, 0, -1991055, -1081365626]\) | \(2640279346000/3087\) | \(1020610974797568\) | \([2]\) | \(311040\) | \(2.1631\) |
Rank
sage: E.rank()
The elliptic curves in class 30492n have rank \(0\).
Complex multiplication
The elliptic curves in class 30492n do not have complex multiplication.Modular form 30492.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.