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SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 11088.by
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11088.by1 | 11088bk2 | \([0, 0, 0, -1072083, 427149970]\) | \(45637459887836881/13417633152\) | \(40064837909741568\) | \([2]\) | \(258048\) | \(2.1648\) | |
11088.by2 | 11088bk1 | \([0, 0, 0, -58323, 8467090]\) | \(-7347774183121/6119866368\) | \(-18273823056986112\) | \([2]\) | \(129024\) | \(1.8182\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11088.by have rank \(1\).
Complex multiplication
The elliptic curves in class 11088.by do not have complex multiplication.Modular form 11088.2.a.by
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.