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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 16224c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16224.i3 | 16224c1 | \([0, -1, 0, -39602, -3005640]\) | \(22235451328/123201\) | \(38058732518976\) | \([2, 2]\) | \(64512\) | \(1.4486\) | \(\Gamma_0(N)\)-optimal |
| 16224.i1 | 16224c2 | \([0, -1, 0, -632792, -193538268]\) | \(11339065490696/351\) | \(867435499008\) | \([2]\) | \(129024\) | \(1.7952\) | |
| 16224.i2 | 16224c3 | \([0, -1, 0, -62417, 877473]\) | \(1360251712/771147\) | \(15246046330564608\) | \([2]\) | \(129024\) | \(1.7952\) | |
| 16224.i4 | 16224c4 | \([0, -1, 0, -17632, -6345080]\) | \(-245314376/6908733\) | \(-17073732926974464\) | \([2]\) | \(129024\) | \(1.7952\) |
Rank
sage: E.rank()
The elliptic curves in class 16224c have rank \(1\).
Complex multiplication
The elliptic curves in class 16224c do not have complex multiplication.Modular form 16224.2.a.c
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
