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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 64974u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
64974.z1 | 64974u1 | \([1, 0, 1, -548140, 145576694]\) | \(154813496529595177/11724454211652\) | \(1379370313546646148\) | \([2]\) | \(1216512\) | \(2.2258\) | \(\Gamma_0(N)\)-optimal |
64974.z2 | 64974u2 | \([1, 0, 1, 528390, 647670286]\) | \(138675717957047543/1620336115431306\) | \(-190630923644377719594\) | \([2]\) | \(2433024\) | \(2.5723\) |
Rank
sage: E.rank()
The elliptic curves in class 64974u have rank \(0\).
Complex multiplication
The elliptic curves in class 64974u do not have complex multiplication.Modular form 64974.2.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.