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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 23120bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
23120.w2 | 23120bb1 | \([0, 0, 0, -93347, 2839714]\) | \(185193/100\) | \(48573594213171200\) | \([2]\) | \(156672\) | \(1.8929\) | \(\Gamma_0(N)\)-optimal |
23120.w1 | 23120bb2 | \([0, 0, 0, -879427, -315208254]\) | \(154854153/1250\) | \(607169927664640000\) | \([2]\) | \(313344\) | \(2.2394\) |
Rank
sage: E.rank()
The elliptic curves in class 23120bb have rank \(1\).
Complex multiplication
The elliptic curves in class 23120bb do not have complex multiplication.Modular form 23120.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.