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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 463680n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
463680.n1 | 463680n1 | \([0, 0, 0, -91668, 10642592]\) | \(28529194119616/123265625\) | \(368069184000000\) | \([2]\) | \(2211840\) | \(1.6483\) | \(\Gamma_0(N)\)-optimal |
463680.n2 | 463680n2 | \([0, 0, 0, -46668, 21100592]\) | \(-470547874952/7779540125\) | \(-185836658724864000\) | \([2]\) | \(4423680\) | \(1.9949\) |
Rank
sage: E.rank()
The elliptic curves in class 463680n have rank \(1\).
Complex multiplication
The elliptic curves in class 463680n do not have complex multiplication.Modular form 463680.2.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.