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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 92416.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
92416.y1 | 92416bj2 | \([0, 0, 0, -72200, -7462592]\) | \(27000000/19\) | \(29290389143552\) | \([2]\) | \(207360\) | \(1.5202\) | |
92416.y2 | 92416bj1 | \([0, 0, 0, -3610, -164616]\) | \(-216000/361\) | \(-8695584276992\) | \([2]\) | \(103680\) | \(1.1736\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 92416.y have rank \(1\).
Complex multiplication
The elliptic curves in class 92416.y do not have complex multiplication.Modular form 92416.2.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.