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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 160080a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
160080.ce2 | 160080a1 | \([0, 1, 0, -107960, 15690900]\) | \(-33974761330806841/6424789539375\) | \(-26315937953280000\) | \([2]\) | \(2113536\) | \(1.8748\) | \(\Gamma_0(N)\)-optimal |
160080.ce1 | 160080a2 | \([0, 1, 0, -1799240, 928305588]\) | \(157264717208387436361/4368589453125\) | \(17893742400000000\) | \([2]\) | \(4227072\) | \(2.2214\) |
Rank
sage: E.rank()
The elliptic curves in class 160080a have rank \(2\).
Complex multiplication
The elliptic curves in class 160080a do not have complex multiplication.Modular form 160080.2.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.