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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 152768.bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 152768.bt1 | 152768bx2 | \([0, 1, 0, -239041, -283565153]\) | \(-5762391987245041/129101095135628\) | \(-33843077483234066432\) | \([]\) | \(3840000\) | \(2.4281\) | |
| 152768.bt2 | 152768bx1 | \([0, 1, 0, -32961, 2966687]\) | \(-15107691357361/5868735488\) | \(-1538453795766272\) | \([]\) | \(768000\) | \(1.6234\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 152768.bt have rank \(1\).
Complex multiplication
The elliptic curves in class 152768.bt do not have complex multiplication.Modular form 152768.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
