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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 32400bt
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
32400.cn2 | 32400bt1 | \([0, 0, 0, -4800, -122000]\) | \(2359296/125\) | \(648000000000\) | \([]\) | \(41472\) | \(1.0232\) | \(\Gamma_0(N)\)-optimal |
32400.cn1 | 32400bt2 | \([0, 0, 0, -64800, 6318000]\) | \(884736/5\) | \(170061120000000\) | \([]\) | \(124416\) | \(1.5725\) |
Rank
sage: E.rank()
The elliptic curves in class 32400bt have rank \(0\).
Complex multiplication
The elliptic curves in class 32400bt do not have complex multiplication.Modular form 32400.2.a.bt
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.