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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 165048c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 165048.bb3 | 165048c1 | \([0, 1, 0, -3879, -54918]\) | \(2725888/1053\) | \(2494108657872\) | \([2]\) | \(202752\) | \(1.0777\) | \(\Gamma_0(N)\)-optimal |
| 165048.bb2 | 165048c2 | \([0, 1, 0, -27684, 1725696]\) | \(61918288/1521\) | \(57641622315264\) | \([2, 2]\) | \(405504\) | \(1.4243\) | |
| 165048.bb1 | 165048c3 | \([0, 1, 0, -440304, 112307856]\) | \(62275269892/39\) | \(5911961263104\) | \([2]\) | \(811008\) | \(1.7709\) | |
| 165048.bb4 | 165048c4 | \([0, 1, 0, 4056, 5483712]\) | \(48668/85683\) | \(-12988578895039488\) | \([2]\) | \(811008\) | \(1.7709\) |
Rank
sage: E.rank()
The elliptic curves in class 165048c have rank \(1\).
Complex multiplication
The elliptic curves in class 165048c do not have complex multiplication.Modular form 165048.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
