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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 452400.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
452400.u1 | 452400u1 | \([0, -1, 0, -199408, -34138688]\) | \(13701674594089/31758480\) | \(2032542720000000\) | \([2]\) | \(3244032\) | \(1.8181\) | \(\Gamma_0(N)\)-optimal |
452400.u2 | 452400u2 | \([0, -1, 0, -127408, -59194688]\) | \(-3573857582569/21617820900\) | \(-1383540537600000000\) | \([2]\) | \(6488064\) | \(2.1646\) |
Rank
sage: E.rank()
The elliptic curves in class 452400.u have rank \(0\).
Complex multiplication
The elliptic curves in class 452400.u do not have complex multiplication.Modular form 452400.2.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.