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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 87120.bm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 87120.bm1 | 87120ct1 | \([0, 0, 0, -29403, 1807498]\) | \(14348907/1100\) | \(215512521523200\) | \([2]\) | \(184320\) | \(1.4950\) | \(\Gamma_0(N)\)-optimal |
| 87120.bm2 | 87120ct2 | \([0, 0, 0, 28677, 8068522]\) | \(13312053/151250\) | \(-29632971709440000\) | \([2]\) | \(368640\) | \(1.8416\) |
Rank
sage: E.rank()
The elliptic curves in class 87120.bm have rank \(1\).
Complex multiplication
The elliptic curves in class 87120.bm do not have complex multiplication.Modular form 87120.2.a.bm
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.
