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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 163800bp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 163800.s1 | 163800bp1 | \([0, 0, 0, -4422675, 1685326750]\) | \(820221748268836/369468094905\) | \(4309475858971920000000\) | \([2]\) | \(7225344\) | \(2.8465\) | \(\Gamma_0(N)\)-optimal |
| 163800.s2 | 163800bp2 | \([0, 0, 0, 15350325, 12619795750]\) | \(17147425715207422/12872524043925\) | \(-300290240896682400000000\) | \([2]\) | \(14450688\) | \(3.1931\) |
Rank
sage: E.rank()
The elliptic curves in class 163800bp have rank \(1\).
Complex multiplication
The elliptic curves in class 163800bp do not have complex multiplication.Modular form 163800.2.a.bp
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
