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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 88725y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
88725.m2 | 88725y1 | \([1, 1, 1, -1415463, -632249844]\) | \(1892819053/55125\) | \(9133953561509765625\) | \([2]\) | \(1797120\) | \(2.4159\) | \(\Gamma_0(N)\)-optimal |
88725.m1 | 88725y2 | \([1, 1, 1, -3337838, 1451604656]\) | \(24820429213/8859375\) | \(1467956822385498046875\) | \([2]\) | \(3594240\) | \(2.7624\) |
Rank
sage: E.rank()
The elliptic curves in class 88725y have rank \(1\).
Complex multiplication
The elliptic curves in class 88725y do not have complex multiplication.Modular form 88725.2.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 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.