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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 123840n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
123840.de2 | 123840n1 | \([0, 0, 0, -45001548, 116182006128]\) | \(1953326569433829507/262451171875\) | \(1354190400000000000000\) | \([2]\) | \(13762560\) | \(3.0737\) | \(\Gamma_0(N)\)-optimal |
123840.de1 | 123840n2 | \([0, 0, 0, -720001548, 7436152006128]\) | \(8000051600110940079507/144453125\) | \(745346396160000000\) | \([2]\) | \(27525120\) | \(3.4203\) |
Rank
sage: E.rank()
The elliptic curves in class 123840n have rank \(0\).
Complex multiplication
The elliptic curves in class 123840n do not have complex multiplication.Modular form 123840.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.