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SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 164934cy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
164934.l1 | 164934cy1 | \([1, -1, 0, -3978, -45900]\) | \(81182737/35904\) | \(3079346808384\) | \([2]\) | \(294912\) | \(1.0920\) | \(\Gamma_0(N)\)-optimal |
164934.l2 | 164934cy2 | \([1, -1, 0, 13662, -352836]\) | \(3288008303/2517768\) | \(-215939194937928\) | \([2]\) | \(589824\) | \(1.4386\) |
Rank
sage: E.rank()
The elliptic curves in class 164934cy have rank \(1\).
Complex multiplication
The elliptic curves in class 164934cy do not have complex multiplication.Modular form 164934.2.a.cy
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.