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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 84800bo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 84800.t2 | 84800bo1 | \([0, -1, 0, -452833, 149105537]\) | \(-2507141976625/889192448\) | \(-3642132267008000000\) | \([]\) | \(1327104\) | \(2.2725\) | \(\Gamma_0(N)\)-optimal |
| 84800.t1 | 84800bo2 | \([0, -1, 0, -39364833, 95075953537]\) | \(-1646982616152408625/38112512\) | \(-156108849152000000\) | \([]\) | \(3981312\) | \(2.8218\) |
Rank
sage: E.rank()
The elliptic curves in class 84800bo have rank \(0\).
Complex multiplication
The elliptic curves in class 84800bo do not have complex multiplication.Modular form 84800.2.a.bo
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
