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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 92575.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
92575.u1 | 92575c1 | \([1, -1, 0, -2151542, 1214813991]\) | \(476196576129/197225\) | \(456193409500390625\) | \([2]\) | \(1824768\) | \(2.3504\) | \(\Gamma_0(N)\)-optimal |
92575.u2 | 92575c2 | \([1, -1, 0, -1820917, 1600653366]\) | \(-288673724529/311181605\) | \(-719781961509716328125\) | \([2]\) | \(3649536\) | \(2.6970\) |
Rank
sage: E.rank()
The elliptic curves in class 92575.u have rank \(0\).
Complex multiplication
The elliptic curves in class 92575.u do not have complex multiplication.Modular form 92575.2.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.