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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 151008.bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 151008.bt1 | 151008j1 | \([0, 1, 0, -351182, 79962012]\) | \(42246001231552/14414517\) | \(1634316553666368\) | \([2]\) | \(1075200\) | \(1.8907\) | \(\Gamma_0(N)\)-optimal |
| 151008.bt2 | 151008j2 | \([0, 1, 0, -302177, 103121775]\) | \(-420526439488/390971529\) | \(-2837012123184205824\) | \([2]\) | \(2150400\) | \(2.2373\) |
Rank
sage: E.rank()
The elliptic curves in class 151008.bt have rank \(1\).
Complex multiplication
The elliptic curves in class 151008.bt do not have complex multiplication.Modular form 151008.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
