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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 79800.bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 79800.bn1 | 79800k4 | \([0, 1, 0, -80808, -7364112]\) | \(1823652903746/328593657\) | \(10514997024000000\) | \([2]\) | \(655360\) | \(1.7933\) | |
| 79800.bn2 | 79800k2 | \([0, 1, 0, -23808, 1299888]\) | \(93280467172/7800849\) | \(124813584000000\) | \([2, 2]\) | \(327680\) | \(1.4467\) | |
| 79800.bn3 | 79800k1 | \([0, 1, 0, -23308, 1361888]\) | \(350104249168/2793\) | \(11172000000\) | \([2]\) | \(163840\) | \(1.1002\) | \(\Gamma_0(N)\)-optimal |
| 79800.bn4 | 79800k3 | \([0, 1, 0, 25192, 6003888]\) | \(55251546334/517244049\) | \(-16551809568000000\) | \([2]\) | \(655360\) | \(1.7933\) |
Rank
sage: E.rank()
The elliptic curves in class 79800.bn have rank \(1\).
Complex multiplication
The elliptic curves in class 79800.bn do not have complex multiplication.Modular form 79800.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
