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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 96192.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
96192.n1 | 96192b2 | \([0, 0, 0, -495660, 134307376]\) | \(70470585447625/4518018\) | \(863406685421568\) | \([2]\) | \(589824\) | \(1.9237\) | |
96192.n2 | 96192b1 | \([0, 0, 0, -29100, 2364208]\) | \(-14260515625/4382748\) | \(-837556185858048\) | \([2]\) | \(294912\) | \(1.5771\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 96192.n have rank \(0\).
Complex multiplication
The elliptic curves in class 96192.n do not have complex multiplication.Modular form 96192.2.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.