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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 361722u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
361722.u2 | 361722u1 | \([1, 1, 1, -1632, 104769]\) | \(-10218313/96192\) | \(-4525437385152\) | \([2]\) | \(995328\) | \(1.1108\) | \(\Gamma_0(N)\)-optimal |
361722.u1 | 361722u2 | \([1, 1, 1, -44952, 3639681]\) | \(213525509833/669336\) | \(31489501805016\) | \([2]\) | \(1990656\) | \(1.4574\) |
Rank
sage: E.rank()
The elliptic curves in class 361722u have rank \(1\).
Complex multiplication
The elliptic curves in class 361722u do not have complex multiplication.Modular form 361722.2.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 Cremona 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 Cremona labels.