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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 141120.bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141120.bh1 | 141120de2 | \([0, 0, 0, -423948, -75564272]\) | \(2185454/625\) | \(2409904496885760000\) | \([2]\) | \(2064384\) | \(2.2337\) | |
141120.bh2 | 141120de1 | \([0, 0, 0, 69972, -7798448]\) | \(19652/25\) | \(-48198089937715200\) | \([2]\) | \(1032192\) | \(1.8872\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 141120.bh have rank \(0\).
Complex multiplication
The elliptic curves in class 141120.bh do not have complex multiplication.Modular form 141120.2.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 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.