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SageMath
E = EllipticCurve("cf1")
E.isogeny_class()
Elliptic curves in class 16830cf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16830.br4 | 16830cf1 | \([1, -1, 1, -31928, 368187]\) | \(4937402992298041/2780405760000\) | \(2026915799040000\) | \([2]\) | \(73728\) | \(1.6272\) | \(\Gamma_0(N)\)-optimal |
| 16830.br2 | 16830cf2 | \([1, -1, 1, -319928, -69212613]\) | \(4967657717692586041/29490113030400\) | \(21498292399161600\) | \([2, 2]\) | \(147456\) | \(1.9738\) | |
| 16830.br1 | 16830cf3 | \([1, -1, 1, -5111528, -4446818373]\) | \(20260414982443110947641/720358602480\) | \(525141421207920\) | \([2]\) | \(294912\) | \(2.3203\) | |
| 16830.br3 | 16830cf4 | \([1, -1, 1, -136328, -148234053]\) | \(-384369029857072441/12804787777021680\) | \(-9334690289448804720\) | \([2]\) | \(294912\) | \(2.3203\) |
Rank
sage: E.rank()
The elliptic curves in class 16830cf have rank \(1\).
Complex multiplication
The elliptic curves in class 16830cf do not have complex multiplication.Modular form 16830.2.a.cf
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
