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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 145794u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
145794.n2 | 145794u1 | \([1, 0, 1, -61201496, 184279786022]\) | \(1064699261301625/4105728\) | \(97762666363218667008\) | \([3]\) | \(11695104\) | \(3.0493\) | \(\Gamma_0(N)\)-optimal |
145794.n1 | 145794u2 | \([1, 0, 1, -84561671, 31003399370]\) | \(2808416463771625/1607794163712\) | \(38283647725252727204216832\) | \([]\) | \(35085312\) | \(3.5986\) |
Rank
sage: E.rank()
The elliptic curves in class 145794u have rank \(1\).
Complex multiplication
The elliptic curves in class 145794u do not have complex multiplication.Modular form 145794.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.