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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 88935.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
88935.u1 | 88935cb2 | \([1, 0, 0, -9863015, -8782206168]\) | \(1115157653/295245\) | \(28093062027645620917065\) | \([2]\) | \(7096320\) | \(3.0160\) | |
88935.u2 | 88935cb1 | \([1, 0, 0, 1550310, -886467933]\) | \(4330747/6075\) | \(-578046543778716479775\) | \([2]\) | \(3548160\) | \(2.6695\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 88935.u have rank \(0\).
Complex multiplication
The elliptic curves in class 88935.u do not have complex multiplication.Modular form 88935.2.a.u
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.