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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 270802j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
270802.j2 | 270802j1 | \([1, 1, 0, 77355, -154723]\) | \(86058173375/49827568\) | \(-29638599475113328\) | \([2]\) | \(2257920\) | \(1.8501\) | \(\Gamma_0(N)\)-optimal |
270802.j1 | 270802j2 | \([1, 1, 0, -309505, -1624791]\) | \(5512402554625/3188422748\) | \(1896548207717306108\) | \([2]\) | \(4515840\) | \(2.1967\) |
Rank
sage: E.rank()
The elliptic curves in class 270802j have rank \(0\).
Complex multiplication
The elliptic curves in class 270802j do not have complex multiplication.Modular form 270802.2.a.j
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.