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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 16830q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16830.e2 | 16830q1 | \([1, -1, 0, -1800, 25600]\) | \(885012508801/137332800\) | \(100115611200\) | \([2]\) | \(18432\) | \(0.83406\) | \(\Gamma_0(N)\)-optimal |
16830.e1 | 16830q2 | \([1, -1, 0, -7920, -244904]\) | \(75370704203521/7497765000\) | \(5465870685000\) | \([2]\) | \(36864\) | \(1.1806\) |
Rank
sage: E.rank()
The elliptic curves in class 16830q have rank \(2\).
Complex multiplication
The elliptic curves in class 16830q do not have complex multiplication.Modular form 16830.2.a.q
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.