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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 257600.bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
257600.bh1 | 257600bh2 | \([0, 1, 0, -968833, -343953537]\) | \(24553362849625/1755162752\) | \(7189146632192000000\) | \([2]\) | \(6193152\) | \(2.3652\) | |
257600.bh2 | 257600bh1 | \([0, 1, 0, 55167, -23441537]\) | \(4533086375/60669952\) | \(-248504123392000000\) | \([2]\) | \(3096576\) | \(2.0186\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 257600.bh have rank \(1\).
Complex multiplication
The elliptic curves in class 257600.bh do not have complex multiplication.Modular form 257600.2.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.