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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 207025bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
207025.bb2 | 207025bb1 | \([1, 0, 0, -33888, 2611517]\) | \(-9317\) | \(-461940705078125\) | \([]\) | \(552960\) | \(1.5522\) | \(\Gamma_0(N)\)-optimal |
207025.bb1 | 207025bb2 | \([1, 0, 0, -879150763, -10033358282858]\) | \(-162677523113838677\) | \(-461940705078125\) | \([]\) | \(20459520\) | \(3.3577\) |
Rank
sage: E.rank()
The elliptic curves in class 207025bb have rank \(1\).
Complex multiplication
The elliptic curves in class 207025bb do not have complex multiplication.Modular form 207025.2.a.bb
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.
\(\left(\begin{array}{rr} 1 & 37 \\ 37 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.