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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 117117.bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 117117.bl1 | 117117g2 | \([1, -1, 0, -4631883333, 121335721233650]\) | \(52652025714902099823/35153041\) | \(7337436637676662636119\) | \([2]\) | \(52475904\) | \(3.9462\) | |
| 117117.bl2 | 117117g1 | \([1, -1, 0, -289435938, 1896705634175]\) | \(-12846937564867743/10503585169\) | \(-2192396118616816686845271\) | \([2]\) | \(26237952\) | \(3.5996\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 117117.bl have rank \(1\).
Complex multiplication
The elliptic curves in class 117117.bl do not have complex multiplication.Modular form 117117.2.a.bl
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
