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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 237538.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
237538.u1 | 237538u1 | \([1, -1, 1, -116671, -15226749]\) | \(3733252610697/23278724\) | \(1095168079135844\) | \([2]\) | \(1209600\) | \(1.7236\) | \(\Gamma_0(N)\)-optimal |
237538.u2 | 237538u2 | \([1, -1, 1, -48081, -33032713]\) | \(-261284780457/9875692358\) | \(-464610647467077398\) | \([2]\) | \(2419200\) | \(2.0702\) |
Rank
sage: E.rank()
The elliptic curves in class 237538.u have rank \(1\).
Complex multiplication
The elliptic curves in class 237538.u do not have complex multiplication.Modular form 237538.2.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.