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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 35574u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35574.bb2 | 35574u1 | \([1, 0, 1, -10482596, -12881562718]\) | \(459206250875/7375872\) | \(2046142037434982581248\) | \([2]\) | \(2027520\) | \(2.8890\) | \(\Gamma_0(N)\)-optimal |
| 35574.bb1 | 35574u2 | \([1, 0, 1, -20917636, 17021087906]\) | \(3648707754875/1660262688\) | \(460573784238880610397792\) | \([2]\) | \(4055040\) | \(3.2356\) |
Rank
sage: E.rank()
The elliptic curves in class 35574u have rank \(1\).
Complex multiplication
The elliptic curves in class 35574u do not have complex multiplication.Modular form 35574.2.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.
