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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 18837r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18837.e3 | 18837r1 | \([0, 0, 1, 145896, -22981473]\) | \(471114356703100928/585612268875179\) | \(-426911344010005491\) | \([]\) | \(233280\) | \(2.0690\) | \(\Gamma_0(N)\)-optimal |
| 18837.e2 | 18837r2 | \([0, 0, 1, -1435944, 1031018292]\) | \(-449167881463536812032/369990050199923699\) | \(-269722746595744376571\) | \([3]\) | \(699840\) | \(2.6183\) | |
| 18837.e1 | 18837r3 | \([0, 0, 1, -133466934, 593483566707]\) | \(-360675992659311050823073792/56219378022244619\) | \(-40983926578216327251\) | \([3]\) | \(2099520\) | \(3.1676\) |
Rank
sage: E.rank()
The elliptic curves in class 18837r have rank \(1\).
Complex multiplication
The elliptic curves in class 18837r do not have complex multiplication.Modular form 18837.2.a.r
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
