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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 6400.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6400.u1 | 6400u2 | \([0, 1, 0, -1583, -24787]\) | \(-2194880\) | \(-200000000\) | \([]\) | \(2880\) | \(0.55013\) | |
| 6400.u2 | 6400u1 | \([0, 1, 0, 17, 13]\) | \(1600\) | \(-320000\) | \([]\) | \(576\) | \(-0.25459\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6400.u have rank \(1\).
Complex multiplication
The elliptic curves in class 6400.u do not have complex multiplication.Modular form 6400.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
