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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 101400.bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 101400.bu1 | 101400j4 | \([0, -1, 0, -914008, -335815988]\) | \(546718898/405\) | \(62555444640000000\) | \([2]\) | \(1474560\) | \(2.1566\) | |
| 101400.bu2 | 101400j3 | \([0, -1, 0, -576008, 166452012]\) | \(136835858/1875\) | \(289608540000000000\) | \([2]\) | \(1474560\) | \(2.1566\) | |
| 101400.bu3 | 101400j2 | \([0, -1, 0, -69008, -2885988]\) | \(470596/225\) | \(17376512400000000\) | \([2, 2]\) | \(737280\) | \(1.8100\) | |
| 101400.bu4 | 101400j1 | \([0, -1, 0, 15492, -350988]\) | \(21296/15\) | \(-289608540000000\) | \([2]\) | \(368640\) | \(1.4634\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 101400.bu have rank \(1\).
Complex multiplication
The elliptic curves in class 101400.bu do not have complex multiplication.Modular form 101400.2.a.bu
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.
