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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 23184bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23184.bs2 | 23184bu1 | \([0, 0, 0, 48021, 9360538]\) | \(4101378352343/15049939968\) | \(-44938879945408512\) | \([2]\) | \(184320\) | \(1.8782\) | \(\Gamma_0(N)\)-optimal |
| 23184.bs1 | 23184bu2 | \([0, 0, 0, -481899, 112482970]\) | \(4144806984356137/568114785504\) | \(1696381659678375936\) | \([2]\) | \(368640\) | \(2.2248\) |
Rank
sage: E.rank()
The elliptic curves in class 23184bu have rank \(0\).
Complex multiplication
The elliptic curves in class 23184bu do not have complex multiplication.Modular form 23184.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
