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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 7650.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7650.u1 | 7650b2 | \([1, -1, 0, -93867, -10225459]\) | \(475854075/39304\) | \(7554888984375000\) | \([]\) | \(51840\) | \(1.7891\) | |
7650.u2 | 7650b1 | \([1, -1, 0, -18867, 999541]\) | \(2816964675/8704\) | \(2295000000000\) | \([]\) | \(17280\) | \(1.2398\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7650.u have rank \(0\).
Complex multiplication
The elliptic curves in class 7650.u do not have complex multiplication.Modular form 7650.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.