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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 303600.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
303600.y1 | 303600y2 | \([0, -1, 0, -126908, 16948812]\) | \(56511149663824/1833565635\) | \(7334262540000000\) | \([2]\) | \(2211840\) | \(1.8181\) | |
303600.y2 | 303600y1 | \([0, -1, 0, 2467, 906312]\) | \(6639190016/1425800475\) | \(-356450118750000\) | \([2]\) | \(1105920\) | \(1.4715\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 303600.y have rank \(0\).
Complex multiplication
The elliptic curves in class 303600.y do not have complex multiplication.Modular form 303600.2.a.y
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 LMFDB 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 LMFDB labels.