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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 160016a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
160016.a2 | 160016a1 | \([0, 0, 0, -857507, -305635870]\) | \(17024594875172176761/13702740137\) | \(56126423601152\) | \([2]\) | \(1492992\) | \(1.9435\) | \(\Gamma_0(N)\)-optimal |
160016.a1 | 160016a2 | \([0, 0, 0, -863347, -301261710]\) | \(17374804109361438921/482665506294457\) | \(1976997913782095872\) | \([2]\) | \(2985984\) | \(2.2900\) |
Rank
sage: E.rank()
The elliptic curves in class 160016a have rank \(0\).
Complex multiplication
The elliptic curves in class 160016a do not have complex multiplication.Modular form 160016.2.a.a
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.