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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 187200.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 187200.u1 | 187200cm1 | \([0, 0, 0, -14700, 146000]\) | \(117649/65\) | \(194088960000000\) | \([2]\) | \(589824\) | \(1.4321\) | \(\Gamma_0(N)\)-optimal |
| 187200.u2 | 187200cm2 | \([0, 0, 0, 57300, 1154000]\) | \(6967871/4225\) | \(-12615782400000000\) | \([2]\) | \(1179648\) | \(1.7787\) |
Rank
sage: E.rank()
The elliptic curves in class 187200.u have rank \(1\).
Complex multiplication
The elliptic curves in class 187200.u do not have complex multiplication.Modular form 187200.2.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.
