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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 159600bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 159600.gs1 | 159600bl1 | \([0, 1, 0, -1044848, -412922412]\) | \(-1231922871794037145/5186378855952\) | \(-531085194849484800\) | \([]\) | \(2488320\) | \(2.2559\) | \(\Gamma_0(N)\)-optimal |
| 159600.gs2 | 159600bl2 | \([0, 1, 0, 2443552, -2174605452]\) | \(15757536948921630455/29083977048526848\) | \(-2978199249769149235200\) | \([]\) | \(7464960\) | \(2.8052\) |
Rank
sage: E.rank()
The elliptic curves in class 159600bl have rank \(0\).
Complex multiplication
The elliptic curves in class 159600bl do not have complex multiplication.Modular form 159600.2.a.bl
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.
