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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 4410.bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4410.bh1 | 4410bi1 | \([1, -1, 1, -14342, -1483009]\) | \(-77626969/182250\) | \(-765912902060250\) | \([]\) | \(24192\) | \(1.5443\) | \(\Gamma_0(N)\)-optimal |
4410.bh2 | 4410bi2 | \([1, -1, 1, 124573, 32856779]\) | \(50872947671/140625000\) | \(-590982177515625000\) | \([3]\) | \(72576\) | \(2.0936\) |
Rank
sage: E.rank()
The elliptic curves in class 4410.bh have rank \(0\).
Complex multiplication
The elliptic curves in class 4410.bh do not have complex multiplication.Modular form 4410.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.