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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 18050f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18050.i3 | 18050f1 | \([1, 0, 1, -1091, -16802]\) | \(-121945/32\) | \(-37636704800\) | \([]\) | \(13500\) | \(0.74612\) | \(\Gamma_0(N)\)-optimal |
18050.i4 | 18050f2 | \([1, 0, 1, 7934, 123988]\) | \(46969655/32768\) | \(-38539985715200\) | \([]\) | \(40500\) | \(1.2954\) | |
18050.i2 | 18050f3 | \([1, 0, 1, -4701, 1463298]\) | \(-25/2\) | \(-918864863281250\) | \([]\) | \(67500\) | \(1.5508\) | |
18050.i1 | 18050f4 | \([1, 0, 1, -1132826, 463994548]\) | \(-349938025/8\) | \(-3675459453125000\) | \([]\) | \(202500\) | \(2.1001\) |
Rank
sage: E.rank()
The elliptic curves in class 18050f have rank \(0\).
Complex multiplication
The elliptic curves in class 18050f do not have complex multiplication.Modular form 18050.2.a.f
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 5 & 15 \\ 3 & 1 & 15 & 5 \\ 5 & 15 & 1 & 3 \\ 15 & 5 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.