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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 152460bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 152460.x2 | 152460bt1 | \([0, 0, 0, -13068, 323433]\) | \(442368/175\) | \(97634978456400\) | \([2]\) | \(368640\) | \(1.3828\) | \(\Gamma_0(N)\)-optimal |
| 152460.x1 | 152460bt2 | \([0, 0, 0, -94743, -10996722]\) | \(10536048/245\) | \(2187023517423360\) | \([2]\) | \(737280\) | \(1.7293\) |
Rank
sage: E.rank()
The elliptic curves in class 152460bt have rank \(0\).
Complex multiplication
The elliptic curves in class 152460bt do not have complex multiplication.Modular form 152460.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
