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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 59850bl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
59850.bk1 | 59850bl1 | \([1, -1, 0, -587727, -173907779]\) | \(-1231922871794037145/5186378855952\) | \(-94521754649725200\) | \([]\) | \(829440\) | \(2.1120\) | \(\Gamma_0(N)\)-optimal |
59850.bk2 | 59850bl2 | \([1, -1, 0, 1374498, -918098924]\) | \(15757536948921630455/29083977048526848\) | \(-530055481709401804800\) | \([]\) | \(2488320\) | \(2.6613\) |
Rank
sage: E.rank()
The elliptic curves in class 59850bl have rank \(1\).
Complex multiplication
The elliptic curves in class 59850bl do not have complex multiplication.Modular form 59850.2.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.