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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 23104.bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23104.bs1 | 23104bz3 | \([0, -1, 0, -1110917, -450312229]\) | \(-50357871050752/19\) | \(-57207791296\) | \([]\) | \(155520\) | \(1.8522\) | |
| 23104.bs2 | 23104bz2 | \([0, -1, 0, -13477, -636189]\) | \(-89915392/6859\) | \(-20652012657856\) | \([]\) | \(51840\) | \(1.3029\) | |
| 23104.bs3 | 23104bz1 | \([0, -1, 0, 963, -829]\) | \(32768/19\) | \(-57207791296\) | \([]\) | \(17280\) | \(0.75362\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 23104.bs have rank \(1\).
Complex multiplication
The elliptic curves in class 23104.bs do not have complex multiplication.Modular form 23104.2.a.bs
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
