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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 223440bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
223440.hf2 | 223440bh1 | \([0, 1, 0, -1141520, -471967980]\) | \(-341370886042369/1817528220\) | \(-875849226464378880\) | \([2]\) | \(4838400\) | \(2.2876\) | \(\Gamma_0(N)\)-optimal |
223440.hf1 | 223440bh2 | \([0, 1, 0, -18287600, -30107252652]\) | \(1403607530712116449/39475350\) | \(19022788412006400\) | \([2]\) | \(9676800\) | \(2.6342\) |
Rank
sage: E.rank()
The elliptic curves in class 223440bh have rank \(0\).
Complex multiplication
The elliptic curves in class 223440bh do not have complex multiplication.Modular form 223440.2.a.bh
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.