Show commands:
SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 35490n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35490.n1 | 35490n1 | \([1, 1, 0, -2056057, -1135105499]\) | \(199144987475642209/102211200000\) | \(493353940060800000\) | \([2]\) | \(806400\) | \(2.3464\) | \(\Gamma_0(N)\)-optimal |
35490.n2 | 35490n2 | \([1, 1, 0, -1704537, -1535346171]\) | \(-113470585236878689/145116562500000\) | \(-700449929924062500000\) | \([2]\) | \(1612800\) | \(2.6930\) |
Rank
sage: E.rank()
The elliptic curves in class 35490n have rank \(0\).
Complex multiplication
The elliptic curves in class 35490n do not have complex multiplication.Modular form 35490.2.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.