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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 125902.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
125902.u1 | 125902s2 | \([1, 1, 1, -14823, -89557]\) | \(2433138625/1387778\) | \(205440949964642\) | \([2]\) | \(394240\) | \(1.4361\) | |
125902.u2 | 125902s1 | \([1, 1, 1, -9533, 352687]\) | \(647214625/3332\) | \(493255582148\) | \([2]\) | \(197120\) | \(1.0896\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 125902.u have rank \(1\).
Complex multiplication
The elliptic curves in class 125902.u do not have complex multiplication.Modular form 125902.2.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.