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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 17160u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17160.o2 | 17160u1 | \([0, 1, 0, 44, 800]\) | \(35969456/1061775\) | \(-271814400\) | \([2]\) | \(6144\) | \(0.29844\) | \(\Gamma_0(N)\)-optimal |
| 17160.o1 | 17160u2 | \([0, 1, 0, -1056, 12240]\) | \(127299503236/6776055\) | \(6938680320\) | \([2]\) | \(12288\) | \(0.64501\) |
Rank
sage: E.rank()
The elliptic curves in class 17160u have rank \(1\).
Complex multiplication
The elliptic curves in class 17160u do not have complex multiplication.Modular form 17160.2.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.
