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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 137904.bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 137904.bk1 | 137904bx1 | \([0, -1, 0, -211137, -37270728]\) | \(13478411517952/304317\) | \(23502080551248\) | \([2]\) | \(645120\) | \(1.6798\) | \(\Gamma_0(N)\)-optimal |
| 137904.bk2 | 137904bx2 | \([0, -1, 0, -203532, -40087620]\) | \(-754612278352/127035441\) | \(-156973007344068864\) | \([2]\) | \(1290240\) | \(2.0264\) |
Rank
sage: E.rank()
The elliptic curves in class 137904.bk have rank \(0\).
Complex multiplication
The elliptic curves in class 137904.bk do not have complex multiplication.Modular form 137904.2.a.bk
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.
