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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 117600.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
117600.u1 | 117600fh4 | \([0, -1, 0, -461008, 120607012]\) | \(11512557512/2835\) | \(2668279320000000\) | \([2]\) | \(1179648\) | \(1.9479\) | |
117600.u2 | 117600fh3 | \([0, -1, 0, -216008, -37540488]\) | \(1184287112/36015\) | \(33897029880000000\) | \([2]\) | \(1179648\) | \(1.9479\) | |
117600.u3 | 117600fh1 | \([0, -1, 0, -32258, 1414512]\) | \(31554496/11025\) | \(1297080225000000\) | \([2, 2]\) | \(589824\) | \(1.6014\) | \(\Gamma_0(N)\)-optimal |
117600.u4 | 117600fh2 | \([0, -1, 0, 96367, 9775137]\) | \(13144256/13125\) | \(-98825160000000000\) | \([2]\) | \(1179648\) | \(1.9479\) |
Rank
sage: E.rank()
The elliptic curves in class 117600.u have rank \(1\).
Complex multiplication
The elliptic curves in class 117600.u do not have complex multiplication.Modular form 117600.2.a.u
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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.