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SageMath
E = EllipticCurve("gu1")
E.isogeny_class()
Elliptic curves in class 320166gu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 320166.gu2 | 320166gu1 | \([1, -1, 1, -72260, 9590991]\) | \(-7414875/2744\) | \(-15441597296033832\) | \([]\) | \(2488320\) | \(1.8165\) | \(\Gamma_0(N)\)-optimal |
| 320166.gu1 | 320166gu2 | \([1, -1, 1, -6297710, 6084634119]\) | \(-545407363875/14\) | \(-709052937062778\) | \([]\) | \(7464960\) | \(2.3658\) | |
| 320166.gu3 | 320166gu3 | \([1, -1, 1, 550285, -96822701]\) | \(4492125/3584\) | \(-14702921702933764608\) | \([]\) | \(7464960\) | \(2.3658\) |
Rank
sage: E.rank()
The elliptic curves in class 320166gu have rank \(1\).
Complex multiplication
The elliptic curves in class 320166gu do not have complex multiplication.Modular form 320166.2.a.gu
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.
\(\left(\begin{array}{rrr} 1 & 3 & 3 \\ 3 & 1 & 9 \\ 3 & 9 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
