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SageMath
E = EllipticCurve("cu1")
E.isogeny_class()
Elliptic curves in class 129472cu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 129472.bx1 | 129472cu1 | \([0, 0, 0, -14051180, -19151031216]\) | \(9869198625/614656\) | \(19107872719802212548608\) | \([2]\) | \(6684672\) | \(3.0268\) | \(\Gamma_0(N)\)-optimal |
| 129472.bx2 | 129472cu2 | \([0, 0, 0, 11103380, -80216241072]\) | \(4869777375/92236816\) | \(-2867375150015319520575488\) | \([2]\) | \(13369344\) | \(3.3734\) |
Rank
sage: E.rank()
The elliptic curves in class 129472cu have rank \(1\).
Complex multiplication
The elliptic curves in class 129472cu do not have complex multiplication.Modular form 129472.2.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.
