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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 75150.bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
75150.bh1 | 75150bi2 | \([1, -1, 1, -85619255, 309617914497]\) | \(-6093832136609347161121/108676727597808690\) | \(-1237895850293789609531250\) | \([]\) | \(12644352\) | \(3.4197\) | |
75150.bh2 | 75150bi1 | \([1, -1, 1, -333005, -318933003]\) | \(-358531401121921/3652290000000\) | \(-41601865781250000000\) | \([]\) | \(1806336\) | \(2.4468\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 75150.bh have rank \(1\).
Complex multiplication
The elliptic curves in class 75150.bh do not have complex multiplication.Modular form 75150.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.