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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 36414.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
36414.y1 | 36414bd1 | \([1, -1, 0, -6837, -203851]\) | \(9869198625/614656\) | \(2201437792512\) | \([2]\) | \(65536\) | \(1.1198\) | \(\Gamma_0(N)\)-optimal |
36414.y2 | 36414bd2 | \([1, -1, 0, 5403, -862363]\) | \(4869777375/92236816\) | \(-330353258738832\) | \([2]\) | \(131072\) | \(1.4663\) |
Rank
sage: E.rank()
The elliptic curves in class 36414.y have rank \(1\).
Complex multiplication
The elliptic curves in class 36414.y do not have complex multiplication.Modular form 36414.2.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.