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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 155526bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
155526.bv2 | 155526bh1 | \([1, 1, 1, -26461, -3831703]\) | \(-2401/6\) | \(-5120384645658534\) | \([]\) | \(1034880\) | \(1.7022\) | \(\Gamma_0(N)\)-optimal |
155526.bv1 | 155526bh2 | \([1, 1, 1, -3655401, 2789363415]\) | \(-6329617441/279936\) | \(-238896666027844562304\) | \([]\) | \(7244160\) | \(2.6752\) |
Rank
sage: E.rank()
The elliptic curves in class 155526bh have rank \(1\).
Complex multiplication
The elliptic curves in class 155526bh do not have complex multiplication.Modular form 155526.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.