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SageMath
E = EllipticCurve("cu1")
E.isogeny_class()
Elliptic curves in class 137904cu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 137904.b2 | 137904cu1 | \([0, -1, 0, -218235, 39196026]\) | \(6774679552/23409\) | \(3971851613160912\) | \([2]\) | \(1597440\) | \(1.8562\) | \(\Gamma_0(N)\)-optimal |
| 137904.b1 | 137904cu2 | \([0, -1, 0, -317100, 243216]\) | \(1298923792/751689\) | \(2040649095472895232\) | \([2]\) | \(3194880\) | \(2.2028\) |
Rank
sage: E.rank()
The elliptic curves in class 137904cu have rank \(0\).
Complex multiplication
The elliptic curves in class 137904cu do not have complex multiplication.Modular form 137904.2.a.cu
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.
