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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 51984.bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 51984.bn1 | 51984ci3 | \([0, 0, 0, -4445715, 29021951698]\) | \(-69173457625/2550136832\) | \(-358238754145976218288128\) | \([]\) | \(4665600\) | \(3.1998\) | |
| 51984.bn2 | 51984ci1 | \([0, 0, 0, -806835, -279037838]\) | \(-413493625/152\) | \(-21352693685649408\) | \([]\) | \(518400\) | \(2.1012\) | \(\Gamma_0(N)\)-optimal |
| 51984.bn3 | 51984ci2 | \([0, 0, 0, 492765, -1060305374]\) | \(94196375/3511808\) | \(-493332634913243922432\) | \([]\) | \(1555200\) | \(2.6505\) |
Rank
sage: E.rank()
The elliptic curves in class 51984.bn have rank \(0\).
Complex multiplication
The elliptic curves in class 51984.bn do not have complex multiplication.Modular form 51984.2.a.bn
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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
