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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 215600p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
215600.w2 | 215600p1 | \([0, 1, 0, 44672, 20808948]\) | \(163667323/3195731\) | \(-192498972886528000\) | \([2]\) | \(2064384\) | \(1.9970\) | \(\Gamma_0(N)\)-optimal |
215600.w1 | 215600p2 | \([0, 1, 0, -915728, 318532948]\) | \(1409825840597/86806489\) | \(5228900671672832000\) | \([2]\) | \(4128768\) | \(2.3435\) |
Rank
sage: E.rank()
The elliptic curves in class 215600p have rank \(0\).
Complex multiplication
The elliptic curves in class 215600p do not have complex multiplication.Modular form 215600.2.a.p
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.